Abstract
The partition function of general \( \mathcal{N} \) = 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 2Re(4πiℱ), 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 \( \mathcal{N} \) = 2* SU(2) Yang-Mills theory and show that the theory does not exhibit phase transitions.
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Russo, J.G. \( \mathcal{N} \) =2 gauge theories and quantum phases. J. High Energ. Phys. 2014, 169 (2014). https://doi.org/10.1007/JHEP12(2014)169
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DOI: https://doi.org/10.1007/JHEP12(2014)169