On Generalized Self-Duality Equations Towards Supersymmetric Quantum Field Theories Of Forms

TL;DR

This paper classifies generalized self-duality equations for p-form gauge fields in dimensions up to 16, identifying conditions under which they can serve as gauge functions for topological quantum field theories, with new insights for dimensions above 9.

Contribution

It extends the classification of self-duality equations for p-form gauge fields to higher dimensions up to 16, generalizing previous work on Yang-Mills fields and establishing criteria for their use in topological theories.

Findings

Classified self-duality equations for p-forms up to D=16.

Identified conditions for invariance under subgroup H of SO(D).

Found potential for new topological quantum field theories in dimensions >9.

Abstract

We classify possible `self-duality' equations for p-form gauge fields in space-time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang-Mills fields (p=1) for D from 5 to 8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T invariant under a sub-group H of SO(D). Second, the representation for the SO(D) curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the `self-duality' equations can be candidates as gauge functions for SO(D)-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for dimensions greater than 9, for various p-form gauge fields.