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4D Chern-Simons theory with auxiliary fields

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arxiv 2407.02204 v3 pith:CW5TH3RG submitted 2024-07-02 hep-th

Osamu Fukushima , Kentaroh Yoshida This is my paper
classification hep-th
keywords auxiliaryafsmfieldsfunctionmodeltheoryboundarychern-simons
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

The auxiliary field sigma model (AFSM) has recently been constructed by Ferko and Smith as deformations of the principal chiral model by including auxiliary fields and the potential term given by an arbitrary univariate function. This AFSM provides an infinite family of integrable sigma models including the original $T\overline{T}$-deformation and the root $T\overline{T}$-deformation. In this paper, we propose a 4D Chern-Simons (CS) theory with auxiliary fields. Then the AFSM is derived from this CS theory with the twist function for the principal chiral model by imposing appropriate boundary conditions for the gauge field and auxiliary fields. We also derive the AFSM with the Wess-Zumino term by deforming the twist function and modifying the boundary conditions.

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Cited by 3 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...

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