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Infinite Family of Integrable Sigma Models Using Auxiliary Fields

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arxiv 2405.05899 v4 pith:OV4NJBYQ submitted 2024-05-09 hep-th math-phmath.MPnlin.SI

Christian Ferko , Liam Smith This is my paper
classification hep-thmath-phmath.MPnlin.SI
keywords modelsauxiliaryclassfamilyfieldinfiniteintegrablesigma
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Time-Dependent Integrability from Gauge Theory, I

    hep-th 2026-07 accept novelty 7.5 of 10

    Spacetime-dependent 4d Chern-Simons theory generates time-dependent integrable field theories whose allowed time dependence coincides with one-loop RG flow while preserving Lax integrability.

  2. Courant-Hilbert deformations of Yang-Baxter sigma models

    hep-th 2026-02 conditional novelty 6.0 of 10

    Yang-Baxter and Courant-Hilbert deformations combine inside 4D Chern-Simons theory: the corrected action equals the master Lagrangian plus half the trace of the energy-momentum tensor.

  3. Soliton Surfaces and the Geometry of Integrable Deformations of the $\mathbb{CP}^{N-1}$ Model

    hep-th 2025-09 conditional novelty 6.0 of 10

    Instanton solutions with vanishing energy-momentum tensor remain solutions under analytic TTbar-like deformations, and the deformed CP^{N-1} model is equivalent to the undeformed model on a field-dependent unit-determ...

  4. Root-$T\bar{T}$ Flows Unify 4D Duality-Invariant Electrodynamics and 2D Integrable Sigma Models

    hep-th 2025-07 conditional novelty 5.0 of 10

    A single generating function encodes both 4D self-dual nonlinear electrodynamics and 2D integrable sigma models, and newly defined gamma flows preserve the root-T Tbar equation across generalized Born-Infeld, logarith...

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