Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models

TL;DR

This paper extends Manin theories to higher dimensions, creating a broad class of third-way-type theories that include integrable deformations of sigma models and gravitational models, with potential applications in mathematical physics.

Contribution

It introduces higher-dimensional generalizations of Manin theories, unifying third-way mechanisms with integrable and gravitational models in a novel framework.

Findings

Constructed higher-dimensional third-way theories.

Derived Yang-Baxter integrable deformations of sigma models.

Connected Manin theories with gravitational models.

Abstract

Manin theories are a class of non-topological deformations of Chern-Simons theories that naturally realise the third-way mechanism and furthermore admit localisation despite not being supersymmetric in the usual sense. In this paper, we extend this construction to higher dimensions, thereby producing a large class of examples of third-way-type theories. Furthermore, the construction naturally yields Yang-Baxter integrable deformations of the principal chiral model as well as gravitational models various dimensions.