Instantons on the 5-sphere and M5-branes

Understand

We calculate the partition functions of supersymmetric gauge theories on S^5, which acquire non-perturbative contributions from instanton loops wrapping its Hopf fiber.

• The instantons on the CP^2 base equivariantly localize to 3 fixed points of SU(3) Cartans.
• Using our results, we study the index of the 6d (2,0) theory.
• We first study the partition functions of maximal SYM with AD(E) gauge groups, which agree with the gravity dual indices on AdS_7 in the large N limits.