Auxiliary Field Deformations of (Semi-)Symmetric Space Sigma Models

TL;DR

This paper extends auxiliary field deformations to symmetric and semi-symmetric space sigma models, creating an infinite family of classically integrable models relevant for string theory and holography, with explicit Lax connections.

Contribution

It generalizes auxiliary field deformations to new classes of sigma models with symmetric or semi-symmetric target spaces, including Wess-Zumino terms, and constructs their Lax connections.

Findings

Established zero-curvature representations for all models in the class.

Generated an infinite family of integrable sigma models.

Extended previous deformations to more general target spaces.

Abstract

We generalize the auxiliary field deformations of the principal chiral model (PCM) introduced in arXiv:2405.05899 and arXiv:2407.16338 to sigma models whose target manifolds are symmetric or semi-symmetric spaces, including a Wess-Zumino term in the latter case. This gives rise to a new infinite family of classically integrable $\mathbb{Z}_2$ and $\mathbb{Z}_4$ coset models of the form which are of interest in applications of integrability to worldsheet string theory and holography. We demonstrate that every theory in this infinite class admits a zero-curvature representation for its equations of motion by exhibiting a Lax connection.