M5-branes, orientifolds, and S-duality

We study the instanton partition functions of 5d maximal super yang-mills theories with all classical gauge groups. they are computed from the adhm quantum mechanics of the d0-d4-o4 systems. our partition functions respect s-dualities of the circle compactified yang-mills theories and various orientifold backgrounds. we also compute and study the s 5 partition functions that correspond to the 6d (2, 0) superconformal indices. our so(2n ) index takes the form of the vacuum character of $$ {mathcal{w}}_d $$ algebra in a special limit, supporting the $$ mathcal{w} $$ algebra conjecture. we propose new indices for (2, 0) theories with outer automorphism twists along the temporal circle, obtained from non-simply-laced syms on s 5.