ON GENERALIZED SELF-DUALITY EQUATIONS TOWARDS SUPERSYMMETRIC QUANTUM-FIELD THEORIES OF FORMS

We classify possible ''self-duality'' equations for p-form gauge field s in space-time dimension up to D = 16, generalizing the pioneering wo rk of Corrigan et al. (1982) on Yang-Mills fields (p = 1) in 4 < D les s 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 mu st decompose under H in a relevant way. When these criteria are fulfil led, the ''self-duality'' equations can be candidates of gauge functio ns for SOD-covariant and H-invariant topological quantum field theorie s. Intriguing possibilities occur for D greater than or equal to 10 fo r various p-form gauge fields.