Chiral observables and S-duality in N = 2* U(N) gauge theories

Understand

We study N = 2* theories with gauge group U(N) and use equivariant localization to calculate the quantum expectation values of the simplest chiral ring elements.

• These are expressed as an expansion in the mass of the adjoint hypermultiplet, with coefficients given by quasi-modular forms of the S-duality group.
• Under the action of this group, we construct combinations of chiral ring elements that transform as modular forms of definite weight.
• As an independent check, we confirm these results by comparing the spectral curves of the associated Hitchin system and the elliptic Calogero-Moser system.