论文标题
五维的二维Yang-Mills理论的五维共同体定位和压缩
Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
论文作者
论文摘要
我们从新的角度重新审视了五维超对称量表理论与二维阳米尔斯理论的变形之间的二元性。我们使用协同学位置技术和Atiyah-Singer索引定理对三个和五个维度进行超对称仪理论的统一处理。我们在统一框架中调查了各种已知结果，并提供了本地化公式的简化推导，以及各种扩展，包括不规则的Seifert振动。我们描述了对四维计算理论的减少，并在几何形状的三维部分是挤压的三个速度（包括扩展到非零区域的扩展）时，对双重二维阳米尔斯理论进行了广泛的描述。挤压参数$ b $产生了对二维Yang-Mills理论的常规$ Q $形式的进一步变形，对于合理的值$ b^2 = p/s $，它与Chern-Simons理论在镜头空间$ L（p，s）$上产生了新的对应关系。
We revisit the duality between five-dimensional supersymmetric gauge theories and deformations of two-dimensional Yang-Mills theory from a new perspective. We give a unified treatment of supersymmetric gauge theories in three and five dimensions using cohomological localization techniques and the Atiyah-Singer index theorem. We survey various known results in a unified framework and provide simplified derivations of localization formulas, as well as various extensions including the case of irregular Seifert fibrations. We describe the reductions to four-dimensional gauge theories, and give an extensive description of the dual two-dimensional Yang-Mills theory when the three-dimensional part of the geometry is a squashed three-sphere, including its extension to non-zero area, and a detailed analysis of the resulting matrix model. The squashing parameter $b$ yields a further deformation of the usual $q$-deformation of two-dimensional Yang-Mills theory, which for rational values $b^2=p/s$ yields a new correspondence with Chern-Simons theory on lens spaces $L(p,s)$.
