带超多重态的N=2理论的等变局域化
Equivariant Localization for N=2 Theories with Hypermultiplets
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中文总结 AI 辅助
Ω背景下的等变局域化技术被应用于CP²上的N=2超对称场论，计算等变关联函数并与低能场论结果对比，确定了不同规范群配分函数的差异因子，还结合S对偶讨论了相关结果。
中文摘要 AI 辅助
Ω背景下的等变局域化是计算凸四维流形上N=2超对称场论配分函数的强大技术。针对复射影平面CP²，我们将等变局域化应用于具有规范群SU(2)和SO(3)、基本表示下N_f个有质量超多重态的超对称杨-米尔斯理论，以及伴随表示下超多重态的N=2*理论。我们计算等变关联函数，它们提供了CP²上瞬子模空间相交数的等变扩展，例如欧拉数和塞格雷不变量。在非等变极限下，我们将结果与低能场论及u平面积分的计算结果进行比较，通过该比较确定了一个特定整体因子，该因子捕捉了紧致四维流形上规范群U(2)与SU(2)或SO(3)配分函数之间的差异。我们还在N_f=4和N=2*理论的S对偶框架下讨论了结果，其中包含N_f=4时味群的三重自同构群。
英文摘要
Equivariant localization in the $Ω$-background is a powerful technique for the evaluation of the partition function of $\mathcal{N}=2$ supersymmetric field theory on a toric four-manifold. For the complex projective plane $\mathbb{CP}^2$, we apply equivariant localization to supersymmetric Yang-Mills theories with gauge groups $SU(2)$ and $SO(3)$ with $N_f$ massive hypermultiplets in the fundamental representation, and the $\mathcal{N}=2^*$ theory with the hypermultiplet in the adjoint representation. We evaluate equivariant correlation functions, which provide an equivariant extension of intersection numbers of moduli spaces of instantons on $\mathbb{CP}^2$, such as Euler numbers and Segre invariants. In the non-equivariant limit, we compare our results with the evaluation using low energy field theory and integration over the $u$-plane. Using this comparison, we identify a specific overall factor, which captures the difference between a partition function for gauge group $U(2)$ and $SU(2)$ or $SO(3)$ on a compact four-manifold. We also discuss our results in the context of $S$-duality of the $N_f=4$ and $\mathcal{N}=2^*$ theory, which includes the triality automorphism group of the flavor group for $N_f=4$.
