AN EXPLICIT COMPUTATION FOR THE BOSE-FERMI EQUIVALENCE ON RIEMANN SURFACES OF GENUS g

Abstract

The instanton sum in the partition function for D bosons on a Riemann surface of genus g, with values in a general D-dimensional torus, TD = RD/ΛD is given explicitly. When the rational metric Q of the lattice, ΛD, is the identity we get the bosonization formula of Alvarez-Gaumé et al. for SO( 2D ). If Q is orthogonal, in the bosonization formula, we get the theta function associated with the quadratic form Q, if Q is generic we get rational Conformal Field Theory. Also we look for conditions on a twisted spin bundle LE, which may ensure that our partition functions arise from some generalized bosonization formulas.