Publications

Order by: publication date number of citations

• Classification of Convergent OPE Channels for Lorentzian CFT Four-Point Functions

  Jiaxin Qiao

  SciPost Phys. 13, 093 (2022) · published 12 October 2022 | Toggle abstract · pdf

  We analyze the convergence properties of operator product expansions (OPE) for Lorentzian CFT four-point functions of scalar operators. We give a complete classification of Lorentzian four-point configurations. All configurations in each class have the same OPE convergence properties in s-, t- and u-channels. We give tables including the information of OPE convergence for all classes. Our work justifies that in a subset of the configuration space, Lorentzian CFT four-point functions are genuine analytic functions. Our results are valid for unitary CFTs in $d\geq2$. Our work also provides some Lorentzian regions where one can do bootstrap analysis in the sense of functions.

  3 citations

• Random features and polynomial rules

  Fabián Aguirre-López, Silvio Franz, Mauro Pastore

  SciPost Phys. 18, 039 (2025) · published 31 January 2025 | Toggle abstract · pdf

  Random features models play a distinguished role in the theory of deep learning, describing the behavior of neural networks close to their infinite-width limit. In this work, we present a thorough analysis of the generalization performance of random features models for generic supervised learning problems with Gaussian data. Our approach, built with tools from the statistical mechanics of disordered systems, maps the random features model to an equivalent polynomial model, and allows us to plot average generalization curves as functions of the two main control parameters of the problem: the number of random features $N$ and the size $P$ of the training set, both assumed to scale as powers in the input dimension $D$. Our results extend the case of proportional scaling between $N$, $P$ and $D$. They are in accordance with rigorous bounds known for certain particular learning tasks and are in quantitative agreement with numerical experiments performed over many order of magnitudes of $N$ and $P$. We find good agreement also far from the asymptotic limits where $D\to ∞$ and at least one between $P/D^K$, $N/D^L$ remains finite.

  3 citations

• ABJ anomaly as a U(1) symmetry and Noether’s theorem

  Valentin Benedetti, Horacio Casini, Javier M. Magan

  SciPost Phys. 18, 041 (2025) · published 3 February 2025 | Toggle abstract · pdf

  The Adler-Bell-Jackiw anomaly determines the violation of chiral symmetry when massless fermions are coupled to an abelian gauge field. In its seminal paper, Adler noticed that a modified chiral $U(1)$ symmetry could still be defined, at the expense of being generated by a non-gauge-invariant conserved current. We show this internal $U(1)$ symmetry has the special feature that it transforms the Haag duality violating sectors (or non local operator classes). This provides a simple unifying perspective on the origin of anomaly quantization, anomaly matching, applicability of Goldstone theorem, and the absence of a Noether current. We comment on recent literature where this symmetry is considered to be either absent or non-invertible. We end by recalling the DHR reconstruction theorem, which states $0$-form symmetries cannot be non-invertible for $d>2$, and argue for a higher form-symmetry reconstruction theorem.

  3 citations

• Two-point boundary correlation functions of dense loop models

  Alexi Morin-Duchesne, Jesper Lykke Jacobsen

  SciPost Phys. 4, 034 (2018) · published 19 June 2018 | Toggle abstract · pdf

  We investigate six types of two-point boundary correlation functions in the dense loop model. These are defined as ratios $Z/Z^0$ of partition functions on the $m\times n$ square lattice, with the boundary condition for $Z$ depending on two points $x$ and $y$. We consider: the insertion of an isolated defect (a) and a pair of defects (b) in a Dirichlet boundary condition, the transition (c) between Dirichlet and Neumann boundary conditions, and the connectivity of clusters (d), loops (e) and boundary segments (f) in a Neumann boundary condition. For the model of critical dense polymers, corresponding to a vanishing loop weight ($\beta = 0$), we find determinant and pfaffian expressions for these correlators. We extract the conformal weights of the underlying conformal fields and find $\Delta = -\frac18$, $0$, $-\frac3{32}$, $\frac38$, $1$, $\tfrac \theta \pi (1+\tfrac{2\theta}\pi)$, where $\theta$ encodes the weight of one class of loops for the correlator of type f. These results are obtained by analysing the asymptotics of the exact expressions, and by using the Cardy-Peschel formula in the case where $x$ and $y$ are set to the corners. For type b, we find a $\log|x-y|$ dependence from the asymptotics, and a $\ln (\ln n)$ term in the corner free energy. This is consistent with the interpretation of the boundary condition of type b as the insertion of a logarithmic field belonging to a rank two Jordan cell. For the other values of $\beta = 2 \cos \lambda$, we use the hypothesis of conformal invariance to predict the conformal weights and find $\Delta = \Delta_{1,2}$, $\Delta_{1,3}$, $\Delta_{0,\frac12}$, $\Delta_{1,0}$, $\Delta_{1,-1}$ and $\Delta_{\frac{2\theta}\lambda+1,\frac{2\theta}\lambda+1}$, extending the results of critical dense polymers. With the results for type f, we reproduce a Coulomb gas prediction for the valence bond entanglement entropy of Jacobsen and Saleur.

  3 citations

• Thermodynamic limit and boundary energy of the spin-1 Heisenberg chain with non-diagonal boundary fields

  Zhihan Zheng, Pei Sun, Xiaotian Xu, Tao Yang, Junpeng Cao, Wen-Li Yang

  SciPost Phys. 12, 071 (2022) · published 22 February 2022 | Toggle abstract · pdf

  The thermodynamic limit and boundary energy of the isotropic spin-1 Heisenberg chain with non-diagonal boundary fields are studied. The finite size scaling properties of the inhomogeneous term in the $T-Q$ relation at the ground state are calculated by the density matrix renormalization group. Based on our findings, the boundary energy of the system in the thermodynamic limit can be obtained from Bethe ansatz equations of a related model with parallel boundary fields. These results can be generalized to the $SU(2)$ symmetric high spin Heisenberg model directly.

  3 citations

• Disordered $\mathcal{N} = (2, 2)$ supersymmetric field theories

  Chi-Ming Chang, Xiaoyang Shen

  SciPost Phys. 16, 140 (2024) · published 30 May 2024 | Toggle abstract · pdf

  We investigate a large class of $\mathcal{N}=(2,2)$ supersymmetric field theories in two dimensions, which contains the Murugan-Stanford-Witten model, and can be naturally regarded as a disordered generalization of the two-dimensional Landau-Ginzburg models. We analyze the two and four-point functions of chiral superfields, and extract from them the central charge, the operator spectrum, and the chaos exponent in these models. Some of the models exhibit a conformal manifold parameterized by the variances of the random couplings. We compute the Zamolodchikov metrics on the conformal manifold, and demonstrate that the chaos exponent varies nontrivally along the conformal manifolds. Finally, we introduce and perform some preliminary analysis of a disordered generalization of the gauged linear sigma models, and discuss the low energy theories as ensemble averages of Calabi-Yau sigma models over complex structure moduli space.

  3 citations

• Spin-polarized two-dimensional electron/hole gases on LiCoO$_2$ layers.

  Santosh Kumar Radha, Walter R. L. Lambrecht

  SciPost Phys. 10, 057 (2021) · published 8 March 2021 | Toggle abstract · pdf

  First-principles calculations show the formation of a 2D spin polarized electron (hole) gas on the Li (CoO$_2$) terminated surfaces of finite slabs down to a monolayer, in remarkable contrast with the bulk band structure, which is stabilized by Li donating its electron to the CoO$_2$ layer forming a Co-$d-t_{2g}^6$ insulator. By mapping the first-principles computational results to a minimal tight-binding models corresponding to a non-chiral 3D generalization of the quadripartite Su-Schrieffer-Heeger (SSH4) model and symmetry analysis, we show that these surface states have topological origin.

  3 citations

• Lifting integrable models and long-range interactions

  Marius de Leeuw, Ana Lucia Retore

  SciPost Phys. 15, 241 (2023) · published 15 December 2023 | Toggle abstract · pdf

  In this paper we discuss a constructive approach to check whether a constant Hamiltonian is Yang-Baxter integrable. We then apply our method to long-range interactions and find the Lax operator and R-matrix of the three-loop SU(2) sector in N=4 SYM. We show that all known integrable long-range deformations of the 6-vertex models of this type can be obtained from a Lax operator and an R-matrix. Finally we discuss what happens at higher loops and highlight some general structures that these models exhibit.

  3 citations

• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings

  Elias Furrer, Horia Magureanu

  SciPost Phys. 17, 073 (2024) · published 5 September 2024 | Toggle abstract · pdf

  Symmetries of Seiberg–Witten (SW) geometries capture intricate physical aspects of the underlying 4d $\mathcal{N} = 2$ field theories. For rank-one theories, these geometries are rational elliptic surfaces whose automorphism group is a semi-direct product between the Coulomb branch (CB) symmetries and the Mordell-Weil group. We study quotients of the SW geometry by subgroups of its automorphism group, which most naturally become gaugings of discrete 0- and 1-form symmetries. Yet, new interpretations of these surgeries become evident when considering 5d $\mathcal{N}=1$ superconformal field theories. There, certain CB symmetries are related to symmetries of the corresponding $(p,q)$-brane web and, as a result, CB surgeries can give rise to (fractional) S-folds. Another novel interpretation of these quotients is the folding across dimensions: circle compactifications of the 5d $E_{2N_f + 1}$ Seiberg theories lead in the infrared to two copies of locally indistinguishable 4d SU(2) SQCD theories with $N_f$ fundamental flavours. This extends earlier results on holonomy saddles, while also reproducing detailed computations of 5d BPS spectra and predicting new 5d and 6d BPS quivers. Finally, we argue that the semi-direct product structure of the automorphism group of the SW geometry includes mixed 't Hooft anomalies between the 0- and 1-form symmetries, and we also present some new results on non-cyclic CB symmetries.

  3 citations

• Two-particle self-consistent approach for broken symmetry phases

  Lorenzo Del Re

  SciPost Phys. 18, 077 (2025) · published 3 March 2025 | Toggle abstract · pdf

  Spontaneous symmetry breaking of interacting fermion systems constitutes a major challenge for many-body theory due to the proliferation of new independent scattering channels once absent or degenerate in the symmetric phase. One example is given by the ferro/antiferromagnetic broken symmetry phase (BSP) of the Hubbard model, where vertices in the spin-transverse and spin-longitudinal channels become independent with a consequent increase in the computational power for their calculation. We generalise the non-perturbative Two-Particle-Self-Consistent method (TPSC) to address broken SU(2) magnetic phases in the Hubbard model, offering an efficient approach that incorporates strong correlations. We show that in the BSP, the sum-rule enforcement of susceptibilities must be accompanied by a modified gap equation resulting in a renormalisation of the order parameter, vertex corrections and the preservation of the gap-less feature of the Goldstone modes. We then apply the theory to the antiferromagnetic phase of the Hubbard model in the cubic lattice at half-filling. We compare our results of double occupancies and staggered magnetisation to the ones obtained using Diagrammatic Monte Carlo showing excellent quantitative agreement. We demonstrate how vertex corrections play a central role in lowering the Higgs resonance with respect to the quasi-particle excitation gap in the spin-longitudinal susceptibility, yielding a well visible Higgs-mode.

  3 citations