Odd-dimensional self-duality for non-Abelian tensor-multiplet in D = 3 + 2 as master theory of integrable-systems

Abstract

We present N=2 supersymmetric non-Abelian duality-symmetry between a tensor multiplet and an extra vector multiplet in D=3+2 dimensions. Our system has the Yang-Mills (YM) vector multiplet (AμI,λI), a tensor-multiplet (BμνI,χI,φI), and an extra vector multiplet (CμI,ρI,σI). The index I=1,2,⋯,dimG is for the adjoint representation of a non-Abelian group G. The AμI is the conventional YM gauge field, BμνI is a non-Abelian tensor field, while φI and σI are scalar fields. The λI,χI and ρI are Majorana fermions in the 2 of Sp(1). The BμνI and CμI-fields have their respective field-strengths defined by GμνρI≡+3D⌊⌈μBνρ⌋⌉I+3fIJKF⌊⌈μνJCρ⌋⌉K and HμνI≡+2D⌊⌈μCν⌋⌉I+mBμνI+fIJKϕJHμνK−fIJKσJFμνK. The duality relationship is HμνI=(1/6)ϵμνρστGρστI−(1/2)fIJK(λ‾JγμνχK), with its super-partner relationships: φI=−σI,χI=−ρI. Since HστI contains mBστI linearly, this is a ‘massive’ self-dual relationship. Interestingly, the closure of supersymmetries shows the intrinsic global scale symmetry: δζ(BμνI,χI,φI,CμI,ρI,σI)=+mζ(BμνI,χI,φI,CμI,ρI,σI). By certain dimensional-reduction scheme into D=2+2, we show that self-dual supersymmetric tensor multiplet is generated. We deduce that our present theory in D=3+2 can serve as the underlying ‘Master Theory’ of a similar system in D=2+2.