Kahler quantization of H*(T2,R) and modular forms

Abstract

Kahler quantization of H1(T2,R) is studied. It is shown that this theory corresponds to a fermionic sigma-model targeting a noncommutative space. By solving the complex-structure moduli independence conditions, the quantum background independent wave function is obtained. We study the transformation of the wave function under modular transformation. It is shown that the transformation rule is characteristic to the operator ordering. Similar results are obtained for Kahler quantization of H2(T,R).