Chiral Tensors of Mixed Young Symmetry

TL;DR

This paper investigates chiral tensors with mixed Young symmetry in specific spacetime dimensions, constructing a variational principle and exploring their properties and role in exotic gravity theories.

Contribution

It introduces a variational principle for chiral tensors of mixed Young symmetry and highlights the importance of prepotentials in their analysis.

Findings

Constructed a variational principle for chiral mixed-symmetry tensors.

Linked chiral tensor actions to non-chiral counterparts.

Discussed dimensional reduction implications.

Abstract

Chiral tensors of mixed Young symmetry, which exist in the same spacetime dimensions $2 + 4n$ where chiral $p$-forms can be defined, are investigated. Such chiral tensors have been argued to play a central role in exotic formulations of gravity in 6 dimensions and possess intriguing properties. A variational principle that yields the chiral equations of motion is explicitly constructed and related to the action for a non-chiral tensor. The use of prepotentials turns out to be essential in our analysis. We also comment on dimensional reduction.