Duality and Massive Gauge Invariant Theories

TL;DR

This paper demonstrates the duality between two massive gauge invariant theories in 3+1 dimensions, linking Stuckelberg and `$B^{}$' formulations, and explores implications for higher-dimensional theories and lower-dimensional models.

Contribution

It establishes a duality relation between Stuckelberg and `$B^{}$' theories using gauging and Lagrange multipliers, and extends the approach to 5D and 2+1D models.

Findings

Duality between Stuckelberg and `$B^{}$' theories shown

Implications for 5D theories discussed

Derivation of the Deser-Jackiw model from Maxwell-Chern-Simons theory

Abstract

Two different massive gauge invariant spin-one theories in $3+1$ dimensions, one Stuckelberg formulation and the other `$B^{\wedge}F$' theory, with Kalb-Ramond field are shown to be related by duality. This is demonstrated by gauging the global symmetry in the model and constraining the corresponding dual field strength to be zero by a Lagrange multiplier, which becomes a field in the dual theory. Implication of this equivalence to the $5$ dimensional theories from which these theories can be obtained is discussed. The self-dual Deser-Jackiw model in $2+1$ dimensions, is also shown to result by applying this procedure to Maxwell-Chern-Simon theory.