Exact results in N=2 gauge theories

Abstract

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. The well known simplicity of the degenerated correlator reflects the fact that for these choices of masses only a very restrictive type of instanton configurations contributes to the gauge theory partition function.

30 pages, 4 figures. reference added, typos corrected. version accepted for publication on JHEP

References in corpus (12)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Correlation functions in conformal Toda field theory I
• Deforming SW curve
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Rigorous Test of Non-conformal Holography: Wilson Loops in N=2* Theory
• Instanton calculus in R-R background and the topological string
• Large N Limit of N=2 SU(N) Gauge Theories from Localization
• Evidence for Large-N Phase Transitions in N=2* Theory
• Deformed N=2 theories, generalized recursion relations and S-duality
• Deformed Seiberg-Witten Curves for ADE Quivers
• Omega-Deformed Seiberg-Witten Effective Action from the M5-brane
• BPS States in the Duality Web of the Omega deformation

Cited by in corpus (11)

• Massive N=2 Gauge Theories at Large N
• A slow review of the AGT correspondence
• Wilson Loops and Chiral Correlators on Squashed Sphere
• Squashing and supersymmetry enhancement in three dimensions
• Alpha- and Omega-Deformations from fluxes in M-Theory
• Wilson Loops and Chiral Correlators on Squashed Spheres
• VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• OPE coefficients in Argyres-Douglas theories
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours