Off- and on-shell harmonic superspaces for 6D SYM theories

It is a brief account of the harmonic superspace formulations of N = (1, 0) and N = (1, 1) SYM theories in six dimensions. The on-shell N = (1, 1) harmonic superspace is argued to provide an efficient tool of constructing candidate counterterms and other invariants of N = (1, 1) SYM. It allows one, e.g., to find out an essential difference between the single- and double-trace dimension d = 10 invariants, which could be capable to explain the absence of the three-loop double-trace (non-planar) counterterms in this theory. The defining superspace constraints of N = (1, 1) SYM are solved in terms of N = (1, 0) harmonic superfields.