N = (2,0) self-dual non-Abelian tensor multiplet in D=3+3 generates N = (1,1) self-dual systems in D=2+2

We formulate an N = (2, 0) system in D = 3 + 3 dimensions consisting of a Yang-Mills (YM)-multiplet ((A) over cap (I)((mu) over cap), (lambda) over cap (I)), a self-dual non-Abelian tensor multiplet ((B) over cap ((mu) over cap(nu) over cap) (I) , (chi) over cap (I),(phi) over cap (I)), and an extra vector multiplet ((C) over cap (I)((mu) over cap) , (sigma) over cap (I)). We next perform the dimensional reductions of this system into D = 2 + 2, and obtain N = (1, 1) systems with a self-dual YM-multiplet (A(mu)(I), lambda(I)), a self-dual tensor multiplet (B-mu nu(I), chi(I), phi(I)), and an extra vector multiplet (C-mu(I), rho(I)). In D = 2 + 2, we reach two distinct theories: 'Theory- I' and 'Theory-II'. The former has the self-dual field-strength H-mu nu((+)I) of C-mu(I) already presented in our recent paper, while the latter has anti-self-dual field strength H-mu nu((-)I) As an application, we show that Theory-II actually generates supersymmetric- KdV equations in D = 1 + 1. Our result leads to a new conclusion that the D = 3 + 3 theory with non-Abelian tensor multiplet can be a 'Grand Master Theory' for self-dual multiplet and self-dual YM-multiplet in D = 2 + 2, that in turn has been conjectured to be the 'Master Theory' for allsupersymmetric integrable theories in D <= 3. (C) 2018 The Author(s). Published by Elsevier B.V.