Spin-½ Bosonization on Compact Surfaces
Spin-½ Bosonization on Compact Surfaces
We extend an existing Bose-Fermi equivalence formula to two-dimensional Euclidean space-times with arbitrary compact topology. The result relates the nonchiral Dirac partition function to that of a scalar field, times a theta function. The proof is a short application of methods from complex geometry and Quillen's determinant constructions.