Exact results in N=2 gauge theories

Understand

We derive exact formulae for the partition function and the expectation values of Wilson/'t Hooft loops, thus directly checking their S-duality transformations.

• We focus on a special class of N=2 gauge theories on S^4 with fundamental matter.
• In particular we show that, for a specific choice of the masses, the matrix model integral defining the gauge theory partition function localizes around a finite set of critical points where it can be explicitly evaluated and written in terms of generalized hypergeometric functions.
• From the AGT perspective the gauge theory partition function, evaluated with this choice of masses, is viewed as a four point correlator involving the insertion of a degenerated field.