Hodge duality transformations in tensor-hierarchy formulations

Abstract

We show in arbitrary space-time dimensions that duality-transformations are possible in general tensor-hierarchy with field-strengths of arbitrary ranks. We first consider the non-Abelian tensor field-strength of the potential , and its compensator field-strength of the potential , where is the adjoint index. We next perform duality transformations into their respective Hodge-dual field-strength of the potential and the field-strength of the potential . As a typical application, we show this to take place in dimensions with an N = 1 supersymmetric set consisting of a Yang–Mills vector-multiplet , an extra vector-multiplet , and a compensating chiral multiplet . The λ I and χ I are Majorana spinors, and is an extra vector with the Proca–Stückelberg scalar CI , while EI is a pseudo-scalar. We perform duality-transformations on and to their Hodge-dual fields and , respectively, ending up with the new set of multiplets and . Another example is the set of multiplets and in . Even though has the maximal 4th rank field-strength, its supersymmetric dual system exists with and after a duality-transformation. Our duality-transformations provide previously-unknown-links among supersymmetric tensor-hierarchy formulations.