Lax Connections in $T\bar{T}$-deformed Integrable Field Theories

Abstract

In this work, we try to construct the Lax connections of $T\bar{T}$-deformed integrable field theories in two different ways. With reasonable assumptions, we make ansatz and find the Lax pairs in the $T\bar{T}$-deformed affine Toda theories and the principal chiral model by solving the Lax equations directly. This way is straightforward but maybe hard to apply for general models. We then make use of the dynamical coordinate transformation to read the Lax connection in the deformed theory from the undeformed one. We find that once the inverse of the transformation is available, the Lax connection can be read easily. We show the construction explicitly for a few classes of scalar models, and find consistency with the ones in the first way.

23 pages

References in corpus (5)

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• $T\bar{T}$-deformed 2D Quantum Field Theories
• Expectation value of composite field $T\bar{T}$ in two-dimensional quantum field theory
• TTbar deformation and the light-cone gauge
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Cited by in corpus (10)

• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
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• Root-$T\overline{T}$ Deformed Boundary Conditions in Holography
• $T\bar{T}$ flow as characteristic flows
• Infinite Family of Integrable Sigma Models Using Auxiliary Fields
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• $T\bar{T}$ and root-$T\bar{T}$ deformations in four-dimensional Chern-Simons theory
• The Courant-Hilbert construction in 4D Chern-Simons theory
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics