Dimensional Reduction of Nonlinear Gauge Theories

TL;DR

This paper explores extending 2D nonlinear gauge theories with additional fields, showing how dimensional reduction from 3D models leads to Courant algebroid realizations and structural modifications.

Contribution

It introduces a novel 2D nonlinear gauge theory with two-form fields derived from 3D models, connecting gauge theories with Courant algebroids.

Findings

Dimensional reduction yields Courant algebroid realizations.

Base structure reduction modifies the target algebroid.

Extension from Poisson sigma models to include two-form fields.

Abstract

We investigate an extension of 2D nonlinear gauge theory from the Poisson sigma model based on Lie algebroid to a model with additional two-form gauge fields. Dimensional reduction of 3D nonlinear gauge theory yields an example of such a model, which provides a realization of Courant algebroid by 2D nonlinear gauge theory. We see that the reduction of the base structure generically results in a modification of the target (algebroid) structure.