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SciPost Physics Vol. 19 issue 6 (December 2025)

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On the role of non-linear latent features in bipartite generative neural networks

Tony Bonnaire, Giovanni Catania, Aurélien Decelle, Beatriz Seoane

SciPost Phys. 19, 141 (2025) · published 1 December 2025 | · pdf

We investigate the phase diagram and memory retrieval capabilities of Restricted Boltzmann Machines (RBMs), an archetypal model of bipartite energy-based neural networks, as a function of the prior distribution imposed on their hidden units—including binary, multi-state, and ReLU-like activations. Drawing connections to the Hopfield model and employing analytical tools from statistical physics of disordered systems, we explore how the architectural choices and activation functions shape the thermodynamic properties of these models. Our analysis reveals that standard RBMs with binary hidden nodes and extensive connectivity suffer from reduced critical capacity, limiting their effectiveness as associative memories. To address this, we examine several modifications, such as introducing local biases and adopting richer hidden unit priors. These adjustments restore ordered retrieval phases and markedly improve recall performance, even at finite temperatures. Our theoretical findings, supported by finite-size Monte Carlo simulations, highlight the importance of hidden unit design in enhancing the expressive power of RBMs.
Scaling laws of shrinkage induced fragmentation phenomena

Roland Szatmári, Akio Nakahara, So Kitsunezaki, Ferenc Kun

SciPost Phys. 19, 142 (2025) · published 1 December 2025 | · pdf

We investigate the shrinkage induced breakup of thin layers of heterogeneous materials attached to a substrate, a ubiquitous natural phenomenon with a wide range of potential applications. Focusing on the evolution of the fragment ensemble, we demonstrate that the system has two distinct phases: damage phase, where the layer is cracked, however, a dominant piece persists retaining the structural integrity of the layer, and a fragmentation phase, where the layer disintegrates into numerous small pieces. Based on finite size scaling we show that the transition between the two phases occurs at a critical damage analogous to continuous phase transitions. At the critical point a fully connected crack network emerges whose structure is controlled by the strength of adhesion to the substrate. In the strong adhesion limit, damage arises from random microcrack nucleation, resembling bond percolation, while weak adhesion facilitates stress concentration and the growth of cracks to large extensions. The critical exponents of the damage to fragmentation transition agree to a reasonable accuracy with those of two-dimensional bond percolation. Our findings provide a novel insights into the mechanism of shrinkage-induced cracking revealing generic scaling laws of the phenomenon.
Entangled universes

Divij Gupta, Matthew Headrick, Martin Sasieta

SciPost Phys. 19, 143 (2025) · published 1 December 2025 | · pdf

We propose a generalization of the RT and HRT holographic entanglement entropy formulas to spacetimes with asymptotically Minkowski as well as asymptotically AdS regions. We postulate that such spacetimes represent entangled states in a tensor product of Hilbert spaces, each corresponding to one asymptotic region. We show that our conjectured formula has the same general properties and passes the same general tests as the standard HRT formula. We provide further evidence for it by showing that in many cases the Minkowski asymptotic regions can be replaced by AdS ones using a domain wall. We illustrate the use of our formula by calculating entanglement entropies between asymptotic regions in Brill-Lindquist spacetimes, finding phase transitions similar to those known to occur in AdS. We construct networks of universes by gluing together Brill-Lindquist spaces along minimal surfaces. Finally, we discuss a variety of possible extensions and generalizations, including to universes with asymptotically de Sitter regions; in the latter case, we identify an ambiguity in the homology condition, leading to two different versions of the HRT formula which we call "orthodox" and "heterodox", with different physical interpretations.
A family of vertex algebras from Argyres-Douglas theory

Heeyeon Kim, Jaewon Song

SciPost Phys. 19, 144 (2025) · published 2 December 2025 | · pdf

We find that multiple vertex algebras can arise from a single 4d $\mathcal{N}=2$ superconformal field theory (SCFT). The connection is given by the BPS monodromy operator $M$, which is a wall-crossing invariant quantity that captures the BPS spectrum on the Coulomb branch. For a class of low-rank Argyres-Douglas theories, we find that the trace of the multiple powers of the monodromy operator Tr$M^N$ yield modular functions that can be identified with the vacuum characters of certain vertex algebra for each $N$. In particular, we realize unitary VOAs of the Deligne-Cvitanović exceptional series type $(A_2)_1$, $(G_2)_1$, $(D_4)_1$, $(F_4)_1$, $(E_6)_1$ from Argyres-Douglas theories. We also find the modular invariant characters of the 'intermediate vertex algebras' $(E_{7\frac{1}{2}})_1$ and $(X_1)_1$. Our analysis allows us to construct 3d $\mathcal{N}=2$ gauge theories that flow to $\mathcal{N}=4$ SCFTs in the IR, whose specialized half-index can be identified with these modular invariant characters.
Generalized symmetry enriched criticality in (3+1)d

Benjamin Moy

SciPost Phys. 19, 145 (2025) · published 3 December 2025 | · pdf

We construct two classes of continuous phase transitions in 3+1 dimensions between gapped phases that break distinct generalized global symmetries. Our analysis focuses on $SU(N)/\mathbb{Z}_N$ gauge theory coupled to $N_f$ flavors of Majorana fermions in the adjoint representation. For $N$ even and sufficiently large odd $N_f$, upon imposing time-reversal symmetry and an $SO(N_f)$ flavor symmetry, the massless theory realizes a quantum critical point between a gapped phase in which a $\mathbb{Z}_N$ one-form symmetry is completely broken and a phase where it is broken to $\mathbb{Z}_2$, leading to $\mathbb{Z}_{N/2}$ topological order. We characterize the possible patterns of symmetry fractionalization in these phases and provide an explicit lattice model that exhibits the transition. The critical point has an enhanced symmetry, which includes non-invertible analogues of time-reversal symmetry. Enforcing a non-invertible time-reversal symmetry and the $SO(N_f)$ flavor symmetry, for $N$ and $N_f$ both odd, we demonstrate that this critical point can appear between a topologically ordered phase and a phase that spontaneously breaks the non-invertible time-reversal symmetry, furnishing an analogue of deconfined quantum criticality for generalized symmetries.
Graviton mass and entanglement islands in low spacetime dimensions

Hao Geng

SciPost Phys. 19, 146 (2025) · published 4 December 2025 | · pdf

It has been conjectured and proven that entanglement island is not consistent with long-range (massless) gravity in a large class of spacetimes, including typical asymptotically anti-de Sitter spacetimes, in high spacetime dimensions. The conjecture and its proof are motivated by the observation that existing constructions of entanglement islands in high dimensions are all in gravitational theories where the graviton is massive for which the standard gravitational Gauss' law doesn't apply. In this letter, we show that this observation persists to lower dimensional cases. We achieve this goal by providing a unified description of the gravitational Gauss' law violation in island models that can work in any dimensions. This unified description teaches us new lessons on entanglement islands and subregion physics in quantum gravity. We focus on the case of the (1+1)-dimensional Jackiw-Teitelboim (JT) gravity for the purpose of demonstration.
Witten index of BMN matrix quantum mechanics

Chi-Ming Chang

SciPost Phys. 19, 147 (2025) · published 5 December 2025 | · pdf

We compute the Witten index of the Berenstein-Maldacena-Nastase matrix quantum mechanics, which counts the number of ground states as well as the difference between the numbers of bosonic and fermionic BPS states with nonzero angular momenta. The Witten index sets a lower bound on the entropy, which exhibits $N^2$ growth that provides strong evidence for the existence of BPS black holes in M-theory, asymptotic to the plane-wave geometry. We also discuss a relation between the Witten index in the infinite $N$ limit and the superconformal index of the Aharony-Bergman-Jafferis-Maldacena theory.
All fractional Shapiro steps in the RSJ model with two Josephson harmonics

Pavel N. Tsarev, Yakov V. Fominov

SciPost Phys. 19, 148 (2025) · published 8 December 2025 | · pdf

Synchronization between the internal dynamics of the superconducting phase in a Josephson junction (JJ) and an external ac signal is a fundamental physical phenomenon, manifesting as constant-voltage Shapiro steps in the current-voltage characteristic. Mathematically, this phase-locking effect is captured by the Resistively Shunted Junction (RSJ) model, an important example of a nonlinear dynamical system. The standard RSJ model considers an overdamped JJ with a sinusoidal (single-harmonic) current-phase relation (CPR) in the current-driven regime with a monochromatic ac component. While this model predicts only integer Shapiro steps, the inclusion of higher Josephson harmonics is known to generate fractional Shapiro steps. In this paper, we show that only two Josephson harmonics in the CPR are sufficient to produce all possible fractional Shapiro steps within the RSJ framework. Using perturbative methods, we analyze the amplitudes of these fractional steps. Furthermore, by introducing a phase shift between the two Josephson harmonics, we reveal an asymmetry between positive and negative fractional steps—a signature of the Josephson diode effect.
Learning the non-Markovian features of subsystem dynamics

Michele Coppola, Mari Carmen Bañuls, Zala Lenarčič

SciPost Phys. 19, 149 (2025) · published 8 December 2025 | · pdf

The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common simplifications often crucial for such a framework. Leveraging tensor network calculations and optimization tools from machine learning, we extract and characterize the dynamical maps for single- and two-site subsystems embedded in an infinite quantum Ising chain after a global quench. We consider three paradigmatic regimes: integrable critical, integrable non-critical, and chaotic. For each we find the optimal time-local representation of the subsystem dynamics at different times. We explore the properties of the learned time-dependent Liouvillians and whether they can be used to forecast the long-time dynamics of local observables beyond the times accessible through direct quantum many-body numerical simulation. Our procedure naturally suggests a novel measure of non-Markovianity based on the distance between the quasi-exact dynamical map and the closest CP-divisible form and reveals that criticality leads to the closest Markovian representation at large times.
Doping lattice non-Abelian quantum Hall states

Zhengyan Darius Shi, Carolyn Zhang, Senthil Todadri

SciPost Phys. 19, 150 (2025) · published 9 December 2025 | · pdf

We study quantum phases of a fluid of mobile charged non-Abelian anyons, which arise upon doping the lattice Moore-Read quantum Hall state at lattice filling $\nu = 1/2$ and its generalizations to the Read-Rezayi ($RR_k$) sequence at $\nu = k/(k+2)$. In contrast to their Abelian counterparts, non-Abelian anyons present unique challenges due to their non-invertible fusion rules and non-Abelian braiding structures. We address these challenges using a Chern-Simons-Ginzburg-Landau (CSGL) framework that incorporates the crucial effect of energy splitting between different anyon fusion channels at nonzero dopant density. For the Moore-Read state, we show that doping the charge $e/4$ non-abelion naturally leads to a fully gapped charge-$2$ superconductor without any coexisting topological order. The chiral central charge of the superconductor depends on details of the interactions determining the splitting of anyon fusion channels. For general $RR_k$ states, our analysis of states obtained by doping the basic non-abelion $a_0$ with charge $e/(k+2)$ reveals a striking even/odd pattern in the Read-Rezayi index $k$. We develop a general physical picture for anyon-driven superconductivity based on charge-flux unbinding, and show how it relates to the CSGL description of doped Abelian quantum Hall states. Finally, as a bonus, we use the CSGL formalism to describe transitions between the $RR_k$ state and a trivial period-$(k+2)$ CDW insulator at fixed filling, driven by the gap closure of the fundamental non-Abelian anyon $a_0$. Notably, for $k=2$, this predicts a period-4 CDW neighboring the Moore-Read state at half-filling, offering a potential explanation of recent numerical observations in models of twisted MoTe$_2$.
Sparsity in the numerical six-point bootstrap

Sebastian Harris

SciPost Phys. 19, 151 (2025) · published 10 December 2025 | · pdf

The paper contributes to an ongoing effort to extend the conformal bootstrap beyond its traditional focus on systems of four-point correlation functions. Recently, it was demonstrated that semidefinite programming can be used to formulate a six-point generalisation of the numerical bootstrap, yielding qualitatively new, rigorous bounds on CFT data. However, the numerical six-point bootstrap requires solving SDPs involving infinite-dimensional matrices, which has so far limited its applicability and hindered scalability in early implementations. This work overcomes the challenges by using sparse matrix decompositions to exploit the banded structure of the underlying SDP. The result is a rewriting of one-dimensional six-point bootstrap problems as effectively two-dimensional standard mixed correlator four-point bootstrap computations. As application, novel bounds whose extremal correlators interpolate between the six-point functions of the generalised free fermion and boson are derived. The extremal interpolations are matched with perturbative deformations of the massive free boson in AdS$_2$.
Algebraic law of local correlations in a driven Rydberg atomic system

Xin Wang, XiaoFeng Wu, Bo Yang, Bo Zhang, Bo Xiong

SciPost Phys. 19, 152 (2025) · published 11 December 2025 | · pdf

Understanding the mechanism behind the buildup of inner correlations is crucial for studying nonequilibrium dynamics in complex, strongly interacting many-body systems. Here we investigate both analytically and numerically the buildup of antiferromagnetic (AF) correlations in a dynamically tuned Ising model with various geometries, realized in a Rydberg atomic system. Through second-order Magnus expansion (ME), we demonstrate quantitative agreement with numerical simulations for diverse configurations including $2 × n$ lattice and cyclic lattice with a star. We find that the AF correlation magnitude at fixed Manhattan distance obeys a universal superposition principle: It corresponds to the algebraic sum of contributions from all shortest paths. This superposition law remains robust against variations in path equivalence, lattice geometries, and quench protocols, establishing a new paradigm for correlation propagation in quantum simulators.
A correspondence between the Rabi model and an Ising model with long-range interactions

Bruno Scheihing-Hitschfeld, Néstor Sepúlveda

SciPost Phys. 19, 153 (2025) · published 15 December 2025 | · pdf

By means of Trotter's formula, we show that transition amplitudes between a class of generalized coherent states in the Rabi model can be understood in terms of a certain Ising model featuring long-range interactions beyond nearest neighbors in its thermodynamic limit. Specifically, we relate the transition amplitudes in the Rabi model to a sum over binary variables of the form of a partition function of an Ising model with a number of spin sites equal to the number of steps in Trotter's formula applied to the real-time evolution of the Rabi model. From this, we show that a perturbative expansion in the energy splitting of the two-level subsystem in the Rabi model is equivalent to an expansion in the number of spin domains in the Ising model. We conclude by discussing how calculations in one model give nontrivial information about the other model, and vice versa, as well as applications and generalizations this correspondence may find.
Von Neumann subfactors and non-invertible symmetries

Xingyang Yu, Hao Y. Zhang

SciPost Phys. 19, 154 (2025) · published 15 December 2025 | · pdf

We use the language of von Neumann subfactors to investigate non-invertible symmetries in two dimensions. A fusion categorical symmetry $\mathcal{C}$, its module category $\mathcal{M}$, and a gauging labeled by an algebra object $\mathcal{A}$ are encoded in the bipartite principal graph of a subfactor. The dual principal graph captures the quantum symmetry $\mathcal{C}'$ obtained by gauging $\mathcal{A}$ in $\mathcal{C}$, as well as a reverse gauging back to $\mathcal{C}$. From a given subfactor $N \subset M$, we derive a quiver diagram that encodes the representations of the associated non-invertible symmetry. We show how this framework provides necessary conditions for admissible gaugings, enabling the construction of generalized orbifold groupoids. To illustrate this strategy, we present three examples: Rep$(D_4)$ as a warm-up, the higher-multiplicity case Rep$(A_4)$ with its associated generalized orbifold groupoid and triality symmetry, and Rep$(A_5)$, where $A_5$ is the smallest non-solvable finite group. For applications to gapless systems, we embed these generalized gaugings as global manipulations on the conformal manifolds of $c=1$ CFTs and uncover new self-dualities in the exceptional $SU(2)_1/A_5$ theory. For $\mathcal{C}$-symmetric TQFTs, we use the subfactor-derived quiver diagrams to characterize gapped phases, describe their vacuum structure, and classify the recently proposed particle-soliton degeneracies.
Precision calibration of calorimeter signals in the ATLAS experiment using an uncertainty-aware neural network

ATLAS Collaboration

SciPost Phys. 19, 155 (2025) · published 16 December 2025 | · pdf

The ATLAS experiment at the Large Hadron Collider explores the use of modern neural networks for a multi-dimensional calibration of its calorimeter signal defined by clusters of topologically connected cells (topo-clusters). The Bayesian neural network (BNN) approach not only yields a continuous and smooth calibration function that improves performance relative to the standard calibration but also provides uncertainties on the calibrated energies for each topo-cluster. The results obtained by using a trained BNN are compared to the standard local hadronic calibration and to a calibration provided by training a deep neural network. The uncertainties predicted by the BNN are interpreted in the context of a fractional contribution to the systematic uncertainties of the trained calibration. They are also compared to uncertainty predictions obtained from an alternative estimator employing repulsive ensembles.
Noncommutative resolutions and CICY quotients from a non-Abelian GLSM

Johanna Knapp, Joseph McGovern

SciPost Phys. 19, 156 (2025) · published 17 December 2025 | · pdf

We discuss a one-parameter non-Abelian GLSM with gauge group $(U(1)× U(1)× U(1))\rtimes\mathbb{Z}_3$ and its associated Calabi-Yau phases. The large volume phase is a free $\mathbb{Z}_3$-quotient of a codimension $3$ complete intersection of degree-$(1,1,1)$ hypersurfaces in $\mathbb{P}^2×\mathbb{P}^2×\mathbb{P}^2$. The associated Calabi-Yau differential operator has a second point of maximal unipotent monodromy, leading to the expectation that the other GLSM phase is geometric as well. However, the associated GLSM phase appears to be a hybrid model with continuous unbroken gauge symmetry and cubic superpotential, together with a Coulomb branch. Using techniques from topological string theory and mirror symmetry we collect evidence that the phase should correspond to a non-commutative resolution, in the sense of Katz-Klemm-Schimannek-Sharpe, of a codimension two complete intersection in weighted projective space with $63$ nodal points, for which a resolution has $\mathbb{Z}_3$-torsion. We compute the associated Gopakumar-Vafa invariants up to genus $11$, incorporating their torsion refinement. We identify two integral symplectic bases constructed from topological data of the mirror geometries in either phase.
Dualities between 2+1d fusion surface models from braided fusion categories

Luisa Eck

SciPost Phys. 19, 157 (2025) · published 17 December 2025 | · pdf

Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories $\mathcal{M}$ over the same braided fusion category $\mathcal{B}$ give rise to dual lattice models. This extends the 1+1d result that dualities in anyon chains are classified by module categories over fusion categories. We analyze two concrete examples: (i) a $\text{Rep}(S_3)$ model with a constrained Hilbert space, dual to the spin-$\tfrac{1}{2}$ XXZ model on the honeycomb lattice, and (ii) a bilayer Kitaev honeycomb model, dual to a spin-$\tfrac{1}{2}$ model with XXZ and Ising interactions. Unlike regular $\mathcal{M}=\mathcal{B}$ fusion surface models, which conserve only 1-form symmetries, models constructed from $\mathcal{M} ≠ \mathcal{B}$ can exhibit both 1-form and 0-form symmetries, including non-invertible ones.
Instanton density operator in lattice QCD from higher category theory

Jing-Yuan Chen

SciPost Phys. 19, 158 (2025) · published 17 December 2025 | · pdf

A natural definition for instanton density operator in lattice QCD has long been desired. We show this problem is, and has to be, solved by higher category theory. The problem is solved by refining at a conceptual level the Yang-Mills theory on lattice, in order to recover the homotopy information in the continuum, which would have been lost if we put the theory on lattice in the traditional way. The refinement needed is a generalization—through the lens of higher category theory—of the familiar process of Villainization that captures winding in lattice XY model and Dirac quantization in lattice Maxwell theory. The apparent difference is that Villainization is in the end described by principal bundles, hence familiar, but more general topological operators can only be captured on the lattice by more flexible structures beyond the usual group theory and fibre bundles, making the language of categories natural and necessary. The key structure we need for our particular problem is called multiplicative bundle gerbe, based upon which we can construct suitable structures to naturally define the 2d Wess-Zumino-Witten term, 3d skyrmion density operator and 4d hedgehog defect for lattice $S^3$ (pion vacua) non-linear sigma model, and the 3d Chern-Simons term, 4d instanton density operator and 5d Yang monopole defect for lattice $SU(N)$ Yang-Mills theory; moreover, the structures behind the non-linear sigma model and the Yang-Mills theory are related via an implicit Yang-Baxter equation. In a broader perspective, higher category theory enables us to rethink more systematically the relation between continuum quantum field theory and lattice quantum field theory. We sketch a proposal towards a general machinery that constructs the suitably refined lattice degrees of freedom for a given non-linear sigma model or gauge theory in the continuum, realizing the desired topological operators on the lattice.
Non-stabilizerness of Sachdev-Ye-Kitaev model

Surajit Bera, Marco Schirò

SciPost Phys. 19, 159 (2025) · published 18 December 2025 | · pdf

We study the non-stabilizerness or quantum magic of the Sachdev-Ye-Kitaev ($\mathrm{SYK}$) model, a prototype example of maximally chaotic quantum matter. We show that the Majorana spectrum of its ground state, encoding the spreading of the state in the Majorana basis, displays a Gaussian distribution as expected for chaotic quantum many-body systems. We compare our results with the case of the $\mathrm{SYK_2}$ model, describing non-chaotic random free fermions, and show that the Majorana spectrum is qualitatively different in the two cases, featuring an exponential Laplace distribution for the $\mathrm{SYK_2}$ model rather than a Gaussian. From the spectrum we extract the Stabilizer Renyi Entropy (SRE) and show that for both models it displays a linear scaling with system size, with a prefactor that is larger for the SYK model, which has therefore higher magic. Finally, we discuss the spreading of quantun magic under unitary dynamics, as described by the evolution of the Majorana spectrum and the Stabilizer Renyi Entropy starting from a stabilizer state. We show that the SRE for the $\mathrm{SYK_2}$ model equilibrates rapidly, but that in the steady-state the interacting chaotic SYK model has more magic than the simple $\mathrm{SYK_2}$. Our results suggest that the Majorana spectrum is qualitatively distinct in chaotic and non-chaotic many-body systems.
Generalized symmetries of non-SUSY and discrete torsion string backgrounds

Noah Braeger, Vivek Chakrabhavi, Jonathan J. Heckman, Max Hübner

SciPost Phys. 19, 160 (2025) · published 18 December 2025 | · pdf

String / M-theory backgrounds with degrees of freedom at a localized singularity provide a general template for generating strongly correlated systems decoupled from lower-dimensional gravity. There are by now several complementary procedures for extracting the associated generalized symmetry data from orbifolds of the form $\mathbb{R}^6 / \Gamma$, including methods based on the boundary topology of the asymptotic geometry, as well as the adjacency matrix for fermionic degrees of freedom in the quiver gauge theory of probe branes. In this paper we show that this match between the two methods also works in non-supersymmetric and discrete torsion backgrounds. In particular, a refinement of geometric boundary data based on Chen-Ruan cohomology matches the expected answer based on quiver data. Additionally, we also show that free (i.e., non-torsion) factors count the number of higher-dimensional branes which couple to the localized singularity. We use this to also extract quadratic pairing terms in the associated symmetry theory (SymTh) for these systems, and explain how these considerations generalize to a broader class of backgrounds.
Non-adiabatic linear response in open quantum systems

Xiaotian Nie, Wei Zheng

SciPost Phys. 19, 161 (2025) · published 19 December 2025 | · pdf

Adiabatic theorem and non-adiabatic corrections have been widely applied in modern quantum technology. Recently, non-adiabatic linear response theory has been developed to probe the many-body correlations in closed systems. In this work, we generalize the non-adiabatic linear response theory to open quantum many-body systems. We show that, similar to the closed case, the first-order deviation from the instantaneous steady state is memoryless—it depends only on the final parameters and not on the initial state or ramping path. When ramping the Hamiltonian, the linear response of observables is governed by the derivative of the retarded Green's function, as in closed systems. In contrast, ramping the dissipation gives rise to a different response, characterized by a high-order correlation function defined in the steady state. Our results offer a compact and physically transparent formulation of non-adiabatic response in open systems, and demonstrate that ramping dynamics can serve as a versatile tool for probing many-body correlations beyond equilibrium.
Monodromies of CFT correlators on the Lorentzian cylinder

Suman Kundu, Shiraz Minwalla, Abhishek Navhal

SciPost Phys. 19, 162 (2025) · published 23 December 2025 | · pdf

While correlators of a CFT are single valued in Euclidean Space, they are multi-valued - and have a complicated sheet structure - in Lorentzian space. Correlators on $R^{1,1}$ are well known to access a finite number of these sheets. In this paper, we demonstrate the spiral nature of lightcones on $S^1 × $ time, which allows the time-ordered correlators of a $CFT_2$ on this spacetime - the Lorentzian cylinder - to access an infinite number of sheets of the correlator. We present a complete classification, both of the sheets accessed as well as of the various distinct causal configurations that lie on a particular sheet. Our construction provides a physical interpretation for an infinite number of sheets of the correlator, while, however, leaving a larger infinity of these sheets uninterpreted.
Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra

Lin Chen, Ling-Yan Hung, Yikun Jiang, Bing-Xin Lao

SciPost Phys. 19, 163 (2025) · published 23 December 2025 | · pdf

We demonstrate that, by utilizing the boundary conformal field theory (BCFT) operator algebra of the Liouville CFT, one can express its path-integral on any Riemann surface as a three dimensional path-integral with appropriate boundary conditions, generalising the recipe for rational CFTs. This serves as a constructive method for deriving the quantum holographic dual of the CFT, which reduces to Einstein gravity in the large central charge limit. As a byproduct, the framework provides an explicit discrete state-sum of a 3D non-chiral topological theory constructed from quantum $6j$ symbols of $\mathcal{U}_q(sl(2,\mathbb{R}))$ with non-trivial boundary conditions, representing a long-sought non-perturbative discrete formulation of 3D pure gravity with negative cosmological constant, at least within a class of three manifolds. This constitutes the first example of an exact holographic tensor network that reproduces a known irrational CFT with a precise quantum gravitational interpretation.
Boundary criticality of complex conformal field theory: A case study in the non-Hermitian 5-state Potts model

Yin Tang, Qianyu Liu, Qicheng Tang, Wei Zhu

SciPost Phys. 19, 164 (2025) · published 24 December 2025 | · pdf

Conformal fields with boundaries give rise to rich critical phenomena that can reveal information about the underlying conformality. While most existing studies focus on Hermitian systems, here we explore boundary critical phenomena in a non-Hermitian quantum 5-state Potts model which exhibits complex conformality in the bulk. We identify free, fixed and mixed conformal boundary conditions and observe the conformal tower structure of energy spectra, supporting the emergence of conformal boundary criticality. We also studied the duality relation between different conformal boundary conditions under the Kramers-Wannier transformation. These findings should facilitate a comprehensive understanding for complex CFTs and stimulate further exploration on the boundary critical phenomena within non-Hermitian strongly-correlated systems.
One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}(\epsilon^2)$

Souvik Bera, Colomba Brancaccio, Dhimiter Canko, Heribertus Bayu Hartanto

SciPost Phys. 19, 165 (2025) · published 24 December 2025 | · pdf

We present analytic expressions for the one-loop QCD helicity amplitudes contributing to top-quark pair production in association with a photon or a jet at the Large Hadron Collider (LHC), evaluated through $\mathcal{O}(\epsilon^2)$ in the dimensional regularisation parameter, $\epsilon$. These amplitudes are required to construct the two-loop hard functions that enter the NNLO QCD computation. The helicity amplitudes are expressed as linear combinations of algebraically independent components of the $\epsilon$-expanded master integrals, with the corresponding rational coefficients written in terms of momentum-twistor variables. We derive differential equations for the pentagon functions, which enable efficient numerical evaluation via generalised power series expansion method.