Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions
Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions
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二维非交换规范理论的瞬子展开
DOI：
10.1007/s00220-003-0964-8
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发表时间：
2002
影响因子：
2.4
通讯作者：
B. Ydri
中科院分区：
文献类型：
--
作者：
Rodrigo Delgadillo;D. O’Connor;B. Ydri
我们证明了二维非对易规范理论是一个精确可解的模型。定义在非对易环面上的规范理论的上同调公式被用来证明它的量子配分函数可以被写成经典解的贡献之和。对于在规范Morita等价下明显不变的任意非对易性参数θ，我们导出了定义在投射模上的Yang-Mills理论的配分函数的一个显式公式.能量观测量是θ的光滑函数。非对易瞬子对路径积分的贡献的建设进行了详细描述。一般来说，有无穷多个规范不等价的固定拓扑荷的贡献，沿着有有限个关于每个瞬子的量子涨落。相关的模空间是一个普通的两个环面的对称产品的组合，其轨道奇异性不是由非交换性解决的。特别地，规范理论的弱耦合极限与θ无关，并且计算了非对易环面上常曲率连接的模空间的辛体积。
We show that noncommutative gauge theory in two dimensions is an exactly solvable model. A cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a sum over contributions from classical solutions. We derive an explicit formula for the partition function of Yang-Mills theory defined on a projective module for an arbitrary noncommutativity parameter θ which is manifestly invariant under gauge Morita equivalence. The energy observables are shown to be smooth functions of θ. The construction of noncommutative instanton contributions to the path integral is described in some detail. In general, there are infinitely many gauge inequivalent contributions of fixed topological charge, along with a finite number of quantum fluctuations about each instanton. The associated moduli spaces are combinations of symmetric products of an ordinary two-torus whose orbifold singularities are not resolved by noncommutativity. In particular, the weak coupling limit of the gauge theory is independent of θ and computes the symplectic volume of the moduli space of constant curvature connections on the noncommutative torus.