标题： 四流形上超对称理论中的无穷共形代数 显示英文标题

标题： Infinite Conformal Algebras in Supersymmetric Theories on Four Manifolds

摘要： 我们研究了一种在Kähler四流形上扭转的超对称理论$M=\Sigma_1 \times \Sigma_2 ,$，其中$\Sigma_{1,2}$是二维黎曼曲面。 我们证明了它在一个BRST上同调中具有“左移”保形应力张量$\Sigma_1$ ($\Sigma_2$)，该张量生成具有常规对易关系的Virasoro代数。 Virasoro代数的中心电荷具有纯粹的几何起源，并且与$\Sigma_2$ ($\Sigma_1$) 曲面的欧拉示性数$\c$成正比。 结果显示，这一构造可以扩展到包括在BRST上同调中实现一个Kac-Moody代数，其级别与欧拉特征量$\c .$成正比。还表明此结构在重整化群下是不变的。 此外，给出了代数$W_{1+\infty}$用自由手征超多重态表示的形式。 我们讨论了瞬子的作用，并探讨了4维Yang-Mills理论的动力学与2维sigma模型动力学之间可能存在的关系。 显示英文摘要

摘要： We study a supersymmetric theory twisted on a K\"ahler four manifold $M=\Sigma_1 \times \Sigma_2 ,$ where $\Sigma_{1,2}$ are 2D Riemann surfaces. We demonstrate that it possesses a "left-moving" conformal stress tensor on $\Sigma_1$ ($\Sigma_2$) in a BRST cohomology, which generates the Virasoro algebra with the conventional commutation relations. The central charge of the Virasoro algebra has a purely geometric origin and is proportional to the Euler characteristic $\c$ of the $\Sigma_2$ ($\Sigma_1$) surface. It is shown that this construction can be extended to include a realization of a Kac-Moody algebra in BRST cohomology with a level proportional to the Euler characteristic $\c .$ This structure is shown to be invariant under renormalization group. A representation of the algebra $W_{1+\infty}$ in terms of a free chiral supermultiplet is also given. We discuss the role of instantons and a possible relation between the dynamics of 4D Yang-Mills theories and those of 2D sigma models.