Self-Duality and New TQFTs for Forms

TL;DR

This paper introduces new topological quantum field theories involving higher-order forms and Yang--Mills fields, derived via dimensional reduction from self-duality equations, expanding the landscape of TQFTs with potential links to interacting field theories.

Contribution

It presents novel TQFTs with interacting higher-order forms obtained through dimensional reduction of self-duality-based theories, highlighting new interactions and symmetry structures.

Findings

New TQFTs with higher-order forms and Yang--Mills fields.

Dimensional reduction links self-duality equations to interacting theories.

Discussion on symmetries and potential connections to interacting field theories.

Abstract

We discuss theories containing higher-order forms in various dimensions. We explain how Chern--Simons-type theories of forms can be defined from TQFTs in one less dimension. We also exhibit new TQFTs with interacting Yang--Mills fields and higher--order forms. They are obtained by the dimensional reduction of TQFTs whose gauge functions are free self-duality equations. Interactions are due to the gauging of global internal symmetries after dimensional reduction. We list possible symmetries and give a brief discussion on the possible relation of such systems to interacting field theories.