A note on higher rank descriptions of massless and massive spin-1 particles

TL;DR

This paper explores alternative higher-rank tensor descriptions of massless and massive spin-1 particles, revealing new dual theories and connections to Kaluza-Klein dimensional reduction.

Contribution

It introduces novel dual formulations of spin-1 theories using higher-rank tensors and investigates their matter couplings and massless limits.

Findings

New dual massless spin-1 theories with rank-3 tensors

Generalized massive spin-1 models with non-symmetric tensors

Massive models derived from higher-rank tensor reduction

Abstract

The Maxwell theory can be written as a first order model with the help of a two-form auxiliary field, such master action allows the proof of duality between $1$-form and $D-3$ forms. Here we show that the replacement of the two-form auxiliary field by an arbitrary (non symmetric) rank-2 tensor leads to a new massless spin-1 dual theory in terms of a partially antisymmetric rank-3 tensor. In the massive spin-1 case we have a non symmetric generalization of the massive two-form theory (Kalb-Ramond). The coupling of the massive non symmetric spin-1 model to matter fields is investigated via master actions. We also show that massive models with severe discontinuity in their massless limit can also be obtained from Kaluza-Klein dimensional reduction of massless higher rank tensors which become Stueckelberg fields after the reduction.