5D Actions for 6D Self-Dual Tensor Field Theory

We present two equivalent five-dimensional actions for six-dimensional (N,0) N=1,2 supersymmetric theories of self-dual tensor whose one spatial dimension is compactified on a circle. The Kaluza-Klein tower consists of a massless vector and infinite number of massive self-dual tensor multiplets living in five-dimensions. The self-duality follows from the equation of motion. Both actions are quadratic in field variables without any auxiliary field. When lifted back to six-dimensions, one of them gives a supersymmetric extension of the bosonic formulation for the chiral two-form tensor by Perry and Schwarz.