Self-dual non-Abelian N = 1 tensor multiplet in D = 2+ 2 dimensions

We present a self-dual non-Abelian N=1 supersymmetric tensor multiplet in D=2+2 space-time dimensions. Our system has three on-shell multiplets: (i) The usual non-Abelian Yang-Mills multiplet (A_μ^I, λ^I) (ii) A non-Abelian tensor multiplet (B_{μν}{}^I, χ^I, φ^I), and (iii) An extra compensator vector multiplet (C_μ^I, ρ^I). Here the index I is for the adjoint representation of a non-Abelian gauge group. The duality symmetry relations are G_{μνρ}{}^I = - ε_{μνρ}{}^σ\nabla_σφ^I, F_{μν}{}^I = + (1/2) ε_{μν}{}^{ρσ} F_{ρσ}{}^I, and H_{μν}{}^I = +(1/2) ε_{μν}{ρσ} H_{ρσ}{}^I, where G and H are respectively the field strengths of B and C. The usual problem with the coupling of the non-Abelian tensor is avoided by non-trivial Chern-Simons terms in the field strengths G_{μνρ}{}^I and H_{μν}{}^I. For an independent confirmation, we re-formulate the component results in superspace. As applications of embedding integrable systems, we show how the {\cal N} = 2, r = 3 and {\cal N} = 3, r = 4 flows of generalized Korteweg-de Vries equations are embedded into our system.

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