Characters of irrelevant deformations

Abstract

We analyse the $T\bar{T}$ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the $1/c$ contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

arXiv comment20 pages

References in corpus (33)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Asymptotic Fragility, Near $Ad{S}_2$ Holography and $T\bar{T}$
• One-loop Partition Functions of 3D Gravity
• Cutoff AdS${}_3$ versus the $T\bar{T}$ deformation
• The $T\overline{T}$ deformation of quantum field theory as random geometry
• $T\bar{T}$ Partition Function from Topological Gravity
• An integrable Lorentz-breaking deformation of two-dimensional CFTs
• A Universal Inequality for CFT and Quantum Gravity
• The $\text{T}\bar{\text{T}}$ perturbation and its geometric interpretation
• Modular invariance and uniqueness of $T\bar{T}$ deformed CFT
• A theory of reparameterizations for AdS${}_3$ gravity
• $T\bar{T}$ and the mirage of a bulk cutoff
• Holography Beyond AdS
• $T\bar{T}$ deformed partition functions
• Quantum scalar field on three-dimensional (BTZ) black hole instanton: heat kernel, effective action and thermodynamics
• A Solvable Irrelevant Deformation of $Ad{S}_3/CF{T}_2$
• Black hole determinants and quasinormal modes
• The Heat Kernel on AdS_3 and its Applications
• $J\bar{T}$ deformed $CF{T}_2$ and String Theory
• Strings on warped AdS${}_3$ via $T\bar{J}$ deformations
• Tweaking one-loop determinants in AdS${}_3$
• $T\bar{T},J\bar{T}$, $T\bar{J}$ Partition Sums From String Theory
• Geometrizing $T\bar{T}$
• Random Boundary Geometry and Gravity Dual of $T\bar{T}$ Deformation
• Quantum Correction to the Entropy of the (2+1)-Dimensional Black Hole
• Ray-Singer Torsion for a Hyperbolic 3-Manifold and Asymptotics of Chern-Simons-Witten Invariant
• $T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS${}_3$ gravity
• Strings, Symmetric Products, $T\bar{T}$ deformations and Hecke Operators
• A Path Integral Realization of Joint $J\bar{T}$, $T\bar{J}$ and $T\bar{T}$ Flows
• A general definition of $J{T}_a$ -- deformed QFTs
• Thermodynamics of $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed conformal field theories
• Symmetries versus the spectrum of $J\bar{T}$-deformed CFTs

Cited by in corpus (3)

• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge