On generalized self-duality equations towards supersymmetric quantum field theories of forms

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) in 4 < D less than or equal to 8. We impose two crucial requirements. First, there should exist a 2 (p + 1)-form T-invariant under a subgroup H of SOD. Second, the representation for the SOD 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 of gauge functions for SOD-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for D greater than or equal to 10 for various p-form gauge fields.