Courant-Hilbert deformations of Yang-Baxter sigma models

TL;DR

This paper introduces integrable deformations of Yang-Baxter sigma models using the Courant-Hilbert construction and four-dimensional Chern-Simons theory, revealing a universal correction term in the deformed action.

Contribution

It demonstrates how Courant-Hilbert deformations can be integrated with Yang-Baxter sigma models through a novel approach involving 4D Chern-Simons theory.

Findings

Deformed actions expressed as sum of master formula Lagrangian and trace of energy-momentum tensor

Courant-Hilbert construction works alongside Yang-Baxter deformations

Universal correction term in the deformed sigma model action

Abstract

We present integrable deformations of Yang-Baxter (YB) sigma models based on the Courant-Hilbert (CH) construction. To this end, we employ the four-dimensional Chern-Simons theory, in which the CH construction is shown in arXiv:2509.22080. As a result, the CH construction works in an intricate way alongside the YB deformations. Remarkably, the resulting deformed action can also be expressed as the sum of the master formula Lagrangian and the trace of the energy-momentum tensor. This result indicates the universality of the correction term.