Relating auxiliary field formulations of $4d$ duality-invariant and $2d$ integrable field theories

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Main Authors: Baglioni, Nicola, Bielli, Daniele, Galli, Michele, Tartaglino-Mazzucchelli, Gabriele
Format: Preprint
Published: 2025
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author Baglioni, Nicola
Bielli, Daniele
Galli, Michele
Tartaglino-Mazzucchelli, Gabriele
author_facet Baglioni, Nicola
Bielli, Daniele
Galli, Michele
Tartaglino-Mazzucchelli, Gabriele
contents Auxiliary field techniques have recently gained interest in four-dimensional non-linear electrodynamics and two-dimensional integrable sigma models. In these settings, coupling a suitable ``seed'' theory to auxiliary fields provides a powerful mechanism to generate infinite families of models while preserving key dynamical properties, such as electromagnetic duality invariance in four dimensions and classical integrability in two dimensions. Deformations induced through auxiliary fields are closely related to $T\bar{T}$-like deformations and, in two dimensions, also to their higher-spin generalisations. In this paper, we analyse and clarify the relations between different auxiliary field formulations in two and four dimensions, showing how they are governed by Legendre transformations of the interaction functions combined with appropriate field redefinitions. In four-dimensional electrodynamics, we establish a correspondence between the auxiliary field model of Russo and Townsend and the Ivanov--Zupnik formalism. In two dimensions, we develop the analogue of the Ivanov--Zupnik $μ$-frame to deform Principal Chiral, symmetric-space, non-Abelian T-dual, and (bi-)Yang-Baxter sigma models. We discuss how integrability is preserved and use properties of the $μ$-frame to further extend known families of integrable deformations.
format Preprint
id arxiv_https___arxiv_org_abs_2512_21982
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Relating auxiliary field formulations of $4d$ duality-invariant and $2d$ integrable field theories
Baglioni, Nicola
Bielli, Daniele
Galli, Michele
Tartaglino-Mazzucchelli, Gabriele
High Energy Physics - Theory
General Relativity and Quantum Cosmology
Mathematical Physics
Exactly Solvable and Integrable Systems
Auxiliary field techniques have recently gained interest in four-dimensional non-linear electrodynamics and two-dimensional integrable sigma models. In these settings, coupling a suitable ``seed'' theory to auxiliary fields provides a powerful mechanism to generate infinite families of models while preserving key dynamical properties, such as electromagnetic duality invariance in four dimensions and classical integrability in two dimensions. Deformations induced through auxiliary fields are closely related to $T\bar{T}$-like deformations and, in two dimensions, also to their higher-spin generalisations. In this paper, we analyse and clarify the relations between different auxiliary field formulations in two and four dimensions, showing how they are governed by Legendre transformations of the interaction functions combined with appropriate field redefinitions. In four-dimensional electrodynamics, we establish a correspondence between the auxiliary field model of Russo and Townsend and the Ivanov--Zupnik formalism. In two dimensions, we develop the analogue of the Ivanov--Zupnik $μ$-frame to deform Principal Chiral, symmetric-space, non-Abelian T-dual, and (bi-)Yang-Baxter sigma models. We discuss how integrability is preserved and use properties of the $μ$-frame to further extend known families of integrable deformations.
title Relating auxiliary field formulations of $4d$ duality-invariant and $2d$ integrable field theories
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
Mathematical Physics
Exactly Solvable and Integrable Systems
url https://arxiv.org/abs/2512.21982