Infinite Family of Integrable Sigma Models Using Auxiliary Fields

Abstract

We introduce a class of $2d$ sigma models which are parameterized by a function of one variable. In addition to the physical field $g$, these models include an auxiliary field $v_{\alpha }$ which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor.

7 pages, LaTeX; v4: final version published in PRL

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Cited by in corpus (7)

• $T\bar{T}$ and root-$T\bar{T}$ deformations in four-dimensional Chern-Simons theory
• 4D Chern-Simons theory with auxiliary fields
• The Courant-Hilbert construction in 4D Chern-Simons theory
• Constraining all possible Korteweg-de Vries type hierarchies
• Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics
• Covariant quantization of the Einstein-Hilbert theory in first-order form
• Integrable models from 4d holomorphic BF theory