Lagrangian interactions within a special class of covariant mixed-symmetry type tensor gauge fields

TL;DR

This paper constructs consistent interactions for a special class of covariant mixed-symmetry tensor gauge fields, revealing dimension-dependent gauge symmetry deformations, with implications for higher-dimensional field theories.

Contribution

It introduces a novel cohomological approach to identify consistent interactions in mixed-symmetry tensor gauge fields, highlighting dimension-specific gauge symmetry deformations.

Findings

In dimensions >4, interactions are gauge invariant and undeformed.

In 4 dimensions, gauge symmetry is deformed by interactions.

The method employs deformation of the master equation and cohomological techniques.

Abstract

Consistent nontrivial interactions within a special class of covariant mixed-symmetry type tensor gauge fields of degree three are constructed from the deformation of the solution to the master equation combined with specific cohomological techniques. In spacetime dimensions strictly greater than four, the only consistent interaction terms are those gauge invariant under the original symmetry. Only in four spacetime dimensions the gauge symmetry is found deformed.