Twisted boundary condition, rectangular matrices, and a non-trivial index in gauge theory on a discretized non-commutative torus(Fundamental Problems and Applications of Quantum Field Theory-Topological Aspects of Quantum Field Theory-)

Abstract

We investigate the topological property of a gauge theory on a discretized 2d non-commutative torus with the twisted boundary condition. The index defined by the Ginsparg-Wilson Dirac operator reproduces the value expected from the index theorem for a constant curvature background, which gives the minimum action. The distribution of the index obtained by Monte Carlo simulation becomes a delta function peaked at the non-zero value in the continuum limit.