$T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS${}_3$ gravity

Abstract

We study the $T\bar{T}$ deformation of the chiral bosons and show the equivalence between the chiral bosons of opposite chiralities and the scalar fields at the Hamiltonian level under the deformation. We also derive the deformed Lagrangian of more generic theories which contain an arbitrary number of chiral bosons to all orders. By using these results, we derive the $T\bar{T}$ deformed boundary action of the AdS${}_3$ gravity theory in the Chern-Simons formulation. We compute the deformed one-loop torus partition function, which satisfies the $T\bar{T}$ flow equation up to the one-loop order. Finally, we calculate the deformed stress tensor of a solution describing a BTZ black hole in the boundary theory, which coincides with the boundary stress tensor derived from the BTZ black hole with a finite cutoff.

arXiv comment29 pages, references added

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Cited by in corpus (17)

• 3D Gravity in a Box
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Infinite pseudo-conformal symmetries of classical $T\bar{T}$, $J\bar{T}$ and $J{T}_a$ - deformed CFTs
• Field Theory of Interacting Boundary Gravitons
• $T\bar{T}$-flow effects on torus partition functions
• Holographic entanglement entropy in $T\overline{T}$-deformed AdS${}_3$
• Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
• $T\bar{T}/J\bar{T}$-deformed WZW models from Chern-Simons AdS${}_3$ gravity with mixed boundary conditions
• Flows in the Space of Interacting Chiral Boson Theories
• $T\overline{T}$ Deformations of nonrelativistic models
• $T\bar{T}$ deformation on multiquantum mechanics and regenesis
• Surface charges in Chern-Simons gravity with $T\bar{T}$ deformation
• Irrelevant Deformations of Chiral Bosons
• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
• Characters of irrelevant deformations
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Modified gauge unfixing formalism and gauge symmetries in the non-commutative chiral bosons theory