Thermodynamics of $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed conformal field theories

Abstract

We compute the Hagedorn temperature of $\mu T\bar{T}+{\epsilon }_{+}J\bar{T}+{\epsilon }_{-}T\bar{J}$ deformed CFT using the universal kernel formula for the thermal partition function. We find a closed analytic expression for the free energy and the Hagedorn temperature as a function of $\mu$, ${\epsilon }_{+}$, and ${\epsilon }_{-}$ for the case of a compact scalar boson by taking the large volume limit. We also compute the Hagedorn temperature for the single trace deformed $Ad{S}_3\times S^1\times T^3\times S^3$ using holographic methods. We identify black hole configurations whose thermodynamics matches the functional dependence on $(\mu ,{\epsilon }_{+},{\epsilon }_{-})$ of the double trace deformed compact scalars.

18 pages

References in corpus (4)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Aspects of Puff Field Theory

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• Entanglement Entropy for $T\bar{T}$, $J\bar{T}$, $T\bar{J}$ deformed holographic CFT
• Exact $T\overline{T}$ deformation of two-dimensional Maxwell theory
• Holographic Complexity of LST and Single Trace $T\bar{T}$
• Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations
• Characters of irrelevant deformations
• Strings in Irrelevant Deformations of $Ad{S}_3/CF{T}_2$
• Comments on the negative specific heat of the $T\bar{T}$ deformed symmetric product CFT
• Non-isometric U-dualities