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arXiv 1411.2602hep-th
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N=2规范理论与量子相

N=2 gauge theories and quantum phases

Jorge G. Russo

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23 pages, 4 figures
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摘要：

四球上一般N = 2超对称SU（2）Yang-Mills理论的配分函数局部化为一个矩阵积分。我们表明，在解压缩极限，并在一定的制度，积分是由一个鞍点。当这发生作用时，自由能精确地以预势$F=-R^2 Re (4πi {\cal F}) $给出，该预势在对偶磁变量$a_D$为零的Seiberg-Witten曲线的奇点处计算。我们还证明了SU（2）规范群下有质量超对称QCD的超共形不动点与量子相变的存在有关。最后，我们讨论了N=2* SU（2）Yang-Mills理论的情形，并证明了该理论不存在相变。

英文摘要：

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 (4πi {\cal 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.

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