Index and winding numbers on T2/ZN orbifolds with magnetic flux

Abstract

We analyze the number of independent chiral zero modes and the winding numbers at the fixed points on T2/ZN (N=2,3,4,6) orbifolds with magnetic flux. In the case of N=2, we derive the index formula n+−n−=M/2+(−V++V−)/4=M/2−V+/2+1 by using the trace formula, where n± are the numbers of the ± chiral zero modes and V± are the sums of the winding numbers at the fixed points on T2/Z2. We also obtain the formula n+−n−=M/N+(−V++V−)/(2N)=M/N−V+/N+1 for N=3,4,6 under an assumption.