An integrable Lorentz-breaking deformation of two-dimensional CFTs

Guica, Monica

doi:10.21468/SciPostPhys.5.5.048

SciPost Physics

An integrable Lorentz-breaking deformation of two-dimensional CFTs

Monica Guica

SciPost Phys. 5, 048 (2018) · published 12 November 2018

doi: 10.21468/SciPostPhys.5.5.048
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Abstract

It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator $T \bar T$, built from the components of the stress tensor, is solvable; in particular, the finite-size spectrum of the deformed theory can be obtained from that of the original CFT through a universal formula. We study a similarly universal, Lorentz-breaking deformation of two-dimensional CFTs that posess a conserved $U(1)$ current, $J$. The deformation takes the schematic form $J \bar T$ and is interesting because it preserves an $SL(2,\mathbb{R}) \times U(1)$ subgroup of the original global conformal symmetries. For the case of a purely (anti)chiral current, we find the finite-size spectrum of the deformed theory and study its thermodynamic properties. We test our predictions in a simple example involving deformed free fermions.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.5.5.048
TI  - An integrable Lorentz-breaking deformation of two-dimensional CFTs
PY  - 2018/11/12
UR  - https://www.scipost.org/SciPostPhys.5.5.048
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 5
IS  - 5
SP  - 048
A1  - Guica, Monica
AB  - It has been recently shown that the deformation of an arbitrary two-dimensional conformal field theory by the composite irrelevant operator $T \bar T$, built from the components of the stress tensor, is solvable; in particular, the finite-size spectrum of the deformed theory can be obtained from that of the original CFT through a universal formula. We study a similarly universal, Lorentz-breaking deformation of two-dimensional CFTs that posess a conserved $U(1)$ current, $J$. The deformation takes the schematic form $J \bar T$ and is interesting because it preserves an $SL(2,\mathbb{R}) \times U(1)$ subgroup of the original global conformal symmetries. For the case of a purely (anti)chiral current, we find the finite-size spectrum of the deformed theory and study its thermodynamic properties. We test our predictions in a simple example involving deformed free fermions.
ER  -

@Article{10.21468/SciPostPhys.5.5.048,
	title={{An integrable Lorentz-breaking deformation of two-dimensional CFTs}},
	author={Monica Guica},
	journal={SciPost Phys.},
	volume={5},
	pages={048},
	year={2018},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.5.5.048},
	url={https://scipost.org/10.21468/SciPostPhys.5.5.048},
}

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Wang et al., Fix the dual geometries of $$T\bar{T}$$ deformed CFT$$_2$$ and highly excited states of CFT$$_2$$
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Griguolo et al., Nonperturbative effects and resurgence in Jackiw-Teitelboim gravity at finite cutoff
Phys. Rev. D 105, 046015 (2022) [Crossref]
Bzowski et al., The holographic interpretation of $$ J\overline{T} $$-deformed CFTs
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Cardy et al., $$ T\overline{T} $$ deformations and the width of fundamental particles
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Conti et al., Conserved currents and T$$ \overline{\mathrm{T}} $$s irrelevant deformations of 2D integrable field theories
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Jeong et al., Entanglement and Rényi entropy of multiple intervals in TT¯ -deformed CFT and holography
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Hernández-Chifflet et al., Flow Equations for Generalized TT¯ Deformations
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Conti et al., The $$ \mathrm{T}\overline{\mathrm{T}} $$ perturbation and its geometric interpretation
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Anninos et al., Charged quantum fields in AdS$_2$
SciPost Phys. 7, 054 (2019) [Crossref]
Chakraborty et al., Thermodynamics of $$ \mathrm{T}\overline{\mathrm{T}} $$, $$ \mathrm{J}\overline{\mathrm{T}} $$, $$ \mathrm{T}\overline{\mathrm{J}} $$ deformed conformal field theories
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Manschot et al., Supersymmetric black holes and TT¯ deformation
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Ashkenazi et al., Linear response of entanglement entropy to $$ T\overline{T} $$ in massive QFTs
J. High Energ. Phys. 2023, 77 (2023) [Crossref]
Araujo, Nonlocal charges from marginal deformations of 2D CFTs: Holographic TT¯ & TJ¯ , and Yang-Baxter deformations
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Grumiller et al., Limits of JT gravity
J. High Energ. Phys. 2021, 134 (2021) [Crossref]
Frolov, $T\overline T$-деформация и калибровка светового конуса
Труды Математического института имени В.А. Стеклова 309, 120 (2020) [Crossref]
Hansen et al., Geometrizing non-relativistic bilinear deformations
J. High Energ. Phys. 2021, 186 (2021) [Crossref]
Jiang et al., Supersymmetric J $$ \overline{T} $$ and T $$ \overline{J} $$ deformations
J. High Energ. Phys. 2020, 140 (2020) [Crossref]
Guica et al., Infinite pseudo-conformal symmetries of classical $T \bar T$, $J \bar T $ and $J T_a$ - deformed CFTs
SciPost Phys. 11, 078 (2021) [Crossref]
Aramini et al., Deforming the ODE/IM correspondence with $$ \textrm{T}\overline{\textrm{T}} $$
J. High Energ. Phys. 2023, 84 (2023) [Crossref]
Hashimoto et al., $$ T\overline{T},J\overline{T},T\overline{J} $$ partition sums from string theory
J. High Energ. Phys. 2020, 80 (2020) [Crossref]
Baggio et al., On $$ T\overline{T} $$ deformations and supersymmetry
J. High Energ. Phys. 2019, 63 (2019) [Crossref]
He et al., Pseudo entropy of primary operators in $$ T\overline{T}/J\overline{T} $$-deformed CFTs
J. High Energ. Phys. 2023, 25 (2023) [Crossref]
Roychowdhury, Analytic integrability for holographic duals with $$ J\overline{T} $$ deformations
J. High Energ. Phys. 2020, 53 (2020) [Crossref]
Asrat, KdV charges and the generalized torus partition sum in TT‾ deformation
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Chakraborty et al., Holographic complexity of LST and single trace $$ T\overline{T} $$
J. High Energ. Phys. 2021, 275 (2021) [Crossref]
Nakayama, Conformal equations that are not Virasoro or Weyl invariant
Lett Math Phys 109, 2255 (2019) [Crossref]
Datta et al., Characters of irrelevant deformations
J. High Energ. Phys. 2021, 162 (2021) [Crossref]
He et al., T $$ \overline{T} $$-flow effects on torus partition functions
J. High Energ. Phys. 2021, 61 (2021) [Crossref]
Sfondrini et al., TT¯ deformations as TsT transformations
Phys. Rev. D 101, 066022 (2020) [Crossref]
Ceschin et al., $$ \mathrm{T}\overline{\mathrm{T}} $$-deformed nonlinear Schrödinger
J. High Energ. Phys. 2021, 121 (2021) [Crossref]
Guica, Symmetries versus the spectrum of $ J\bar T$-deformed CFTs
SciPost Phys. 10, 065 (2021) [Crossref]
Gorbenko et al., dS/dS and $$ T\overline{T} $$
J. High Energ. Phys. 2019, 85 (2019) [Crossref]
Grieninger, Entanglement entropy and $$ T\overline{T} $$ deformations beyond antipodal points from holography
J. High Energ. Phys. 2019, 171 (2019) [Crossref]
Cotler et al., A theory of reparameterizations for AdS3 gravity
J. High Energ. Phys. 2019, 79 (2019) [Crossref]
Nakayama, Holographic dual of conformal field theories with very special TJ¯ deformations
Phys. Rev. D 100, 086011 (2019) [Crossref]
Esper et al., $$ T\overline{T} $$ deformations of non-relativistic models
J. High Energ. Phys. 2021, 101 (2021) [Crossref]
Ebert et al., T $$ \overline{T} $$ deformation in SCFTs and integrable supersymmetric theories
J. High Energ. Phys. 2021, 82 (2021) [Crossref]
He et al., Correlation functions, entanglement and chaos in the $$ T\overline{T}/J\overline{T} $$-deformed CFTs
J. High Energ. Phys. 2020, 88 (2020) [Crossref]
Jiang et al., TT¯ deformations with N=(0,2) supersymmetry
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Ferko et al., Sequential flows by irrelevant operators
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Apolo et al., TsT, black holes, and $$ T\overline{T} $$ + $$ J\overline{T} $$ + $$ T\overline{J} $$
J. High Energ. Phys. 2022, 177 (2022) [Crossref]
He et al., Correlation functions of CFTs on a torus with a TT¯ deformation
Phys. Rev. D 102, 026023 (2020) [Crossref]
Babaei-Aghbolagh et al., Marginal TT¯ -like deformation and modified Maxwell theories in two dimensions
Phys. Rev. D 106, 086022 (2022) [Crossref]
van Dongen et al., Emergence and correspondence for string theory black holes
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 69, 112 (2020) [Crossref]
Nastase et al., A $$ T\overline{T} $$-like deformation of the Skyrme model and the Heisenberg model of nucleon-nucleon scattering
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Borsato et al., Marginal deformations of WZW models and the classical Yang–Baxter equation
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Ferko et al., Root- TT¯ Deformations in Two-Dimensional Quantum Field Theories
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Ojeda et al., Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies
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Araujo et al., Holographic integration of $$ T\overline{T} $$ & $$ J\overline{T} $$ via O(d, d)
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He et al., Genus two correlation functions in CFTs with $$T\bar T$$ deformation
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Song et al., Structure constants from modularity in warped CFT
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Castro-Alvaredo et al., Form factors and correlation functions of $$ \textrm{T}\overline{\textrm{T}} $$-deformed integrable quantum field theories
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Nastase et al., Soliton, breather and shockwave solutions of the Heisenberg and the $$ T\overline{T} $$ deformations of scalar field theories in 1+1 dimensions
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Chang et al., TT¯ flows and (2, 2) supersymmetry
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Detournay et al., Warped flatland
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Aharony et al., Modular covariance and uniqueness of $$ J\overline{T} $$ deformed CFTs
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Guica, On correlation functions in $J\bar{T}$ -deformed CFTs
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Ferko et al., ModMax oscillators and root- TT¯ -like flows in supersymmetric quantum mechanics
Phys. Rev. D 108, 046013 (2023) [Crossref]
De Nardis et al., Correlation functions and transport coefficients in generalised hydrodynamics
J. Stat. Mech. 2022, 014002 (2022) [Crossref]
Aharony et al., Modular invariance and uniqueness of $$ T\overline{T} $$ deformed CFT
J. High Energ. Phys. 2019, 86 (2019) [Crossref]
Chakraborty et al., $$ T\overline{T} $$ and $$ J\overline{T} $$ deformations in quantum mechanics
J. High Energ. Phys. 2020, 99 (2020) [Crossref]
Kruthoff et al., On the flow of states under $T\overline{T}$
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Pozsgay et al., $$ T\overline{T} $$-deformation and long range spin chains
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Aguilera-Damia et al., A path integral realization of joint $$ J\overline{T} $$, $$ T\overline{J} $$ and $$ T\overline{T} $$ flows
J. High Energ. Phys. 2020, 85 (2020) [Crossref]
Babaei-Aghbolagh et al., $$ T\overline{T} $$-like flows in non-linear electrodynamic theories and S-duality
J. High Energ. Phys. 2021, 187 (2021) [Crossref]
Chakraborty et al., Entanglement entropy for $$ \mathrm{T}\overline{\mathrm{T}} $$, $$ \mathrm{J}\overline{\mathrm{T}} $$, $$ \mathrm{T}\overline{\mathrm{J}} $$ deformed holographic CFT
J. High Energ. Phys. 2021, 96 (2021) [Crossref]
Jiang, A pedagogical review on solvable irrelevant deformations of 2D quantum field theory
Commun. Theor. Phys. 73, 057201 (2021) [Crossref]
Asrat et al., TT¯ , the entanglement wedge cross section, and the breakdown of the split property
Phys. Rev. D 102, 045009 (2020) [Crossref]
He et al., TT¯/JT¯ -deformed WZW models from Chern-Simons AdS3 gravity with mixed boundary conditions
Phys. Rev. D 103, 126019 (2021) [Crossref]
Anous et al., A general definition of $JT_a$ -- deformed QFTs
SciPost Phys. 10, 096 (2021) [Crossref]
Roychowdhury, Penrose limit for holographic duals of JT¯ deformations
J. Phys. A: Math. Theor. 54, 335401 (2021) [Crossref]
Nakayama, Very special TJ¯ deformed CFT
Phys. Rev. D 99, 085008 (2019) [Crossref]
Rosenhaus et al., Integrability and renormalization under TT¯
Phys. Rev. D 102, 065009 (2020) [Crossref]
Dorey et al., Geometric aspects of the ODE/IM correspondence
J. Phys. A: Math. Theor. 53, 223001 (2020) [Crossref]
Medenjak et al., Thermal transport in TT¯ -deformed conformal field theories: From integrability to holography
Phys. Rev. D 103, 066012 (2021) [Crossref]
Córdova et al., Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model
J. High Energ. Phys. 2022, 35 (2022) [Crossref]
He, Note on higher-point correlation functions of the $$T\bar T$$ or $$J\bar T$$ deformed CFTs
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Aggarwal et al., Near-extremal limits of warped black holes
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Frolov, $ \newcommand{\ov}{\over} \boldsymbol {T\overline{T}}$ , $ \newcommand{\om}{\omega} \newcommand{\w}{\omega} \boldsymbol{\widetilde J J}$ , JT and $ \newcommand{\om}{\omega} \newcommand{\w}{\omega} \boldsymbol {\widetilde JT}$ deformations
J. Phys. A: Math. Theor. 53, 025401 (2020) [Crossref]
Jiang et al., Irrelevant deformations with boundaries and defects
J. Stat. Mech. 2022, 043102 (2022) [Crossref]
Shyam et al., $$ T\overline{T} $$ deformed scattering happens within matrices
J. High Energ. Phys. 2023, 132 (2023) [Crossref]
Apolo et al., On the universal behavior of $$ T\overline{T} $$-deformed CFTs: single and double-trace partition functions at large c
J. High Energ. Phys. 2023, 210 (2023) [Crossref]
Le Floch et al., KdV charges in TTbar theories and new models with super-Hagedorn behavior
SciPost Phys. 7, 043 (2019) [Crossref]
Ebrahim et al., Holographic entanglement entropy and mutual information in deformed field theories at finite temperature
Phys. Rev. D 107, 086010 (2023) [Crossref]
Aggarwal et al., Boundary conditions for warped AdS3 in quadratic ensemble
J. High Energ. Phys. 2022, 13 (2022) [Crossref]
Jiang, Expectation value of $$ \mathrm{T}\overline{\mathrm{T}} $$ operator in curved spacetimes
J. High Energ. Phys. 2020, 94 (2020) [Crossref]
Chaturvedi et al., A note on the complex SYK model and warped CFTs
J. High Energ. Phys. 2018, 101 (2018) [Crossref]
Asrat, Entropic c–functions in TT‾,JT‾,TJ‾ deformations
Nuclear Physics B 960, 115186 115186 (2020) [Crossref]
Sun et al., Note on the Rényi entropy of 2D perturbed fermions
Phys. Rev. D 99, 106008 (2019) [Crossref]
Apolo et al., Heating up holography for single-trace $$ J\overline{T} $$ deformations
J. High Energ. Phys. 2020, 141 (2020) [Crossref]
Banerjee et al., Entanglement entropy for TT deformed CFT in general dimensions
Nuclear Physics B 948, 114775 114775 (2019) [Crossref]
Post et al., A universe field theory for JT gravity
J. High Energ. Phys. 2022, 118 (2022) [Crossref]

Ontology / Topics

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Conformal field theory (CFT) Free fermions Lorentz invariance

Author / Affiliations: mappings to Contributors and Organizations

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¹ ² ³ ⁴ Monica Guica

Funders for the research work leading to this publication

European Research Council [ERC]
Knut och Alice Wallenbergs Stiftelse (Knut and Alice Wallenberg Foundation) (through Organization: Knut och Alice Wallenbergs Stiftelse / Knut and Alice Wallenberg Foundation)
Vetenskapsrådet / Swedish Research Council