$T\bar{T}$ and root-$T\bar{T}$ deformations in four-dimensional Chern-Simons theory

Abstract

The four-dimensional Chern-Simons (CS) theory provides a systematic procedure for realizing two-dimensional integrable field theories. It is therefore a natural question to ask whether integrable deformations of the theories can be realized in the four-dimensional CS theory. In this work, we study $T\bar{T}$ and root-$T\bar{T}$ deformations of two-dimensional integrable field theories, formulated in terms of dynamical coordinate transformations, within the framework of four-dimensional CS theory coupled to disorder defects. We illustrate our procedure in detail for the degenerate $\mathcal{E}$-model, a specific construction that captures and unifies a broad range of integrable systems, including the principal chiral model.

51 pages, 2 figures; v2: reference updated; v3: published version

References in corpus (17)

• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Integrable Deformations of Strings on Symmetric Spaces
• Emergence of non-linear electrodynamic theories from $T\bar{T}$-like deformations
• Root-$T\overline{T}$ Deformations in Two-Dimensional Quantum Field Theories
• Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $\sqrt{T\bar{T}}$ deformations
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• 4-dimensional Chern-Simons theory and integrable field theories
• Thermodynamic geometry and complexity of black holes in theories with broken translational invariance
• The Chern-Simons Origin of Superstring Integrability
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Infinite Family of Integrable Sigma Models Using Auxiliary Fields
• Integrable degenerate $\mathcal{E}$-models from 4d Chern-Simons theory
• Lax Connections in $T\bar{T}$-deformed Integrable Field Theories
• 4D Chern-Simons theory with auxiliary fields
• $T\bar{T}$ Deformations in Curved Space from 4D Chern-Simons Theory
• Comments on the negative specific heat of the $T\bar{T}$ deformed symmetric product CFT

Cited by in corpus (2)

• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT
• Integrable models from 4d holomorphic BF theory