Pre-quantization of the moduli space of flat G-bundles over a surface

Abstract

For a simply connected, compact, simple Lie group G , the moduli space of flat G -bundles over a closed surface Σ is known to be pre-quantizable at integer levels. For non-simply connected G , however, integrality of the level is not sufficient for pre-quantization, and this paper determines the obstruction–namely a certain cohomology class in H 3 ( G 2 ; Z ) –that places further restrictions on the underlying level. The levels that admit a pre-quantization of the moduli space are determined explicitly for all non-simply connected, compact, simple Lie groups G .