N=2 gauge theories and quantum phases

Abstract

The partition function of general N = 2 supersymmetric SU(2) Yang-Mills theories on a four-sphere localizes to a matrix integral. We show that in the decompactification limit, and in a certain regime, the integral is dominated by a saddle point. When this takes effect, the free energy is exactly given in terms of the prepotential, $F=-R^{2}Re(4\pi i\mathcal{F})$, evaluated at the singularity of the Seiberg-Witten curve where the dual magnetic variable $a_D$ vanishes. We also show that the superconformal fixed point of massive supersymmetric QCD with gauge group SU(2) is associated with the existence of a quantum phase transition. Finally, we discuss the case of N=2* SU(2) Yang-Mills theory and show that the theory does not exhibit phase transitions.

23 pages, 4 figures

References in corpus (3)

• SU(N) gauge theories at large N
• N=2* Super-Yang-Mills Theory at Strong Coupling
• Modular anomaly equations in N=2* theories and their large-N limit

Cited by in corpus (3)

• N = 2* Phase Transitions and Holography
• Large $N_c$ from Seiberg-Witten Curve and Localization
• Higher Rank Wilson Loops in N = 2* Super-Yang-Mills Theory