Sasakians and the Geometry of a Mass Term

TL;DR

This paper explores how mass terms for gauge fields in various dimensions can be described using geometric structures like WZW actions and Sasakian structures, unifying different cases under a common framework.

Contribution

It introduces a geometric framework based on Sasakian structures to describe dynamically generated mass terms in three-dimensional gauge theories.

Findings

Mass terms in 2D gauge theories relate to WZW actions.

Finite temperature effects in 4D generate screening masses via WZW actions.

A new geometric approach using Sasakian structures describes 3D mass generation.

Abstract

A gauge-invariant mass term for nonabelian gauge fields in two dimensions can be expressed as the Wess-Zumino-Witten (WZW) action. Hard thermal loops in the gauge theory in four dimensions at finite temperatures generate a screening mass for some components of the gauge field. This can be expressed in terms of the WZW action using the bundle of complex structures (for Euclidean signature) or the bundle of lightcones over Minkowski space. We show that a dynamically generated mass term in three dimensions can be put within the same general framework using using the bundle of Sasakian structures.