Tensor global symmetries and the Stueckelberg mechanism for tensor fields

TL;DR

This paper explores tensor global symmetries and develops a Stueckelberg mechanism for mixed symmetry tensor fields, revealing gauge-invariant currents and anomalies in linearized gravity.

Contribution

It introduces a Stueckelberg framework for mixed symmetry tensors and identifies associated gauge-invariant currents linked to tensor global symmetries.

Findings

Constructed gauge-invariant Stueckelberg actions for massive tensor fields.

Identified conserved currents of mixed symmetry related to global symmetries.

Discovered a 't Hooft anomaly in linearized gravity through nonminimal coupling.

Abstract

We investigate the concept of tensor global symmetries, featuring conserved currents of mixed symmetry and higher spin Nambu-Goldstone bosons. We develop a Stueckelberg mechanism for mixed symmetry tensor fields at the linearized level, focusing on the massive graviton, the massive $(2,1)$ Curtright field and the massive $(2,2)$ field. Counting degrees of freedom, we identify the set of fields that necessarily appear in the gauge invariant Stueckelberg action in each case. These fields transform under shift symmetries and they are a vector and a scalar in the first case, a graviton, a Kalb-Ramond field and a vector in the second case and a Curtright field and a graviton in the third case. The analysis results in gauge invariant and fully conserved currents of mixed symmetry for the corresponding gauge theories, which are linked to their tensor global symmetries and they can be minimally coupled to suitable background fields. Viewing the graviton and the Kalb-Ramond field as Nambu-Goldstone bosons for constant symmetric and antisymmetric shift symmetries, we use a nonminimal coupling to uncover a 't Hooft anomaly in linearized gravity.