On the Classical Integrability of Root-$T\overline{T}$ Flows

Abstract

The Root-$T\overline{T}$ flow was recently introduced as a universal and classically marginal deformation of any two-dimensional translation-invariant field theory. The flow commutes with the (irrelevant) $T\overline{T}$ flow and it can be integrated explicitly for a large class of actions, leading to non-analytic Lagrangians reminiscent of the four-dimensional Modified-Maxwell theory (ModMax). It is not a priori obvious whether the Root-$T\overline{T}$ flow preserves integrability, like it is the case for the $T\overline{T}$ flow. In this paper we demonstrate that this is the case for a large class of classical models by explicitly constructing a deformed Lax connection. We discuss the principal chiral model and the non-linear sigma models on symmetric and semi-symmetric spaces, without or with Wess-Zumino term. We also construct Lax connections for the two-parameter families of theories deformed by both Root-$T\overline{T}$ and $T\overline{T}$ for all of these models.

34 pages; LaTeX; references added; comment added

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Cited by in corpus (17)

• Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows
• Interacting Chiral Form Field Theories and $T\overline{T}$-like Flows in Six and Higher Dimensions
• Geometric formulation of generalized root-$T\bar{T}$ deformations
• Stress Tensor Flows, Birefringence in Non-Linear Electrodynamics, and Supersymmetry
• Massive gravity generalization of $T\overline{T}$ deformations
• Root-$T\overline{T}$ Deformed Boundary Conditions in Holography
• Infinite Family of Integrable Sigma Models Using Auxiliary Fields
• Quantization of the ModMax Oscillator
• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
• $T\overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry
• Flows in the Space of Interacting Chiral Boson Theories
• $T\bar{T}$ and root-$T\bar{T}$ deformations in four-dimensional Chern-Simons theory
• Waves and strings in an interacting conformal chiral 2-form theory in six dimensions
• The Courant-Hilbert construction in 4D Chern-Simons theory
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• On $\sqrt{T\overline{T}}$ deformed pathways: CFT to CCFT