$T\bar{T}$ deformations as TsT transformations

Abstract

The relationship between $T\bar{T}$ deformations and the uniform light-cone gauge, first noted in arXiv:1804.01998, provides a powerful generating technique for deformed models. We recall this construction, distinguishing between changes of the gauge frame, which do not affect the theory, and genuine deformations. We investigate the geometric interpretation of the latter and argue that they affect the global features of the geometry before gauge fixing. Exploiting a formal relation between uniform light-cone gauge and static gauge in a T-dual frame, we interpret such a change as a TsT transformation involving the two light-cone coordinates. In the static-gauge picture, the $T\bar{T}$ CDD factor then has a natural interpretation as a Drinfel'd-Reshetikhin twist of the worldsheet S matrix. To illustrate these ideas, we find the geometries yielding a $T\bar{T}$ deformation of the worldsheet S matrix of pp-wave and Lin-Lunin-Maldacena backgrounds.

30 pages, 1 figure; v2: further examples (section 5) and discussion of JTbar deformations (appendix B) added, references added

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• Flow equations for generalised $T\bar{T}$ deformations
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• On the Classical Integrability of Root-$T\overline{T}$ Flows
• Non-relativistic duality and $T\bar{T}$ deformations
• Geometrizing non-relativistic bilinear deformations
• $T\bar{T}$-deformation and Liouville gravity
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Maximally Supersymmetric RG Flows in 4D and Integrability
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• Lax Connections in $T\bar{T}$-deformed Integrable Field Theories
• Exact $T\overline{T}$ deformation of two-dimensional Maxwell theory
• $T\bar{T}$ deformed soft theorem
• Non-equilibrium dynamics in Holography
• Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs
• Canonical maps and integrability in $T\bar{T}$ deformed 2d CFTs
• $T\bar{T}$ deformations and the pp wave correspondence
• Moving holographic boundaries
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• On exactly solvable Yang-Baxter models and enhanced symmetries
• On Current-Squared Flows and ModMax Theories