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 (AˆμˆI,λˆI), a self-dual non-Abelian tensor multiplet (BˆμˆνˆI,χˆI,φˆI), and an extra vector multiplet (CˆμˆI,ρˆI). 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 (AμI,λI), a self-dual tensor multiplet (BμνI,χI,φI), and an extra vector multiplet (CμI,ρI). In D=2+2, we reach two distinct theories: ‘Theory-I’ and ‘Theory-II’. The former has the self-dual field-strength Hμν(+)I of CμI already presented in our recent paper, while the latter has anti-self-dual field strength Hμν(−)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 all supersymmetric integrable theories in D≤3.