Twisted boundary condition, rectangular matrices, and a non-trivial index in gauge theory on a discretized non-commutative torus

摘要

We investigate the topological property of a gauge theory on a discietized 2d non-commutative torus with the twisted boundary condition. The index defined by the Ginsparg-Wilson Diiac 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.