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

TL;DR

This paper explores Kahler quantization of certain cohomology groups of tori, revealing connections to fermionic sigma-models, noncommutative spaces, and modular transformations, with implications for quantum background independence.

Contribution

It introduces a novel analysis of Kahler quantization on H*(T2,R), linking it to fermionic sigma-models and noncommutative geometry, and examines modular transformation properties.

Findings

Quantum background independent wave function derived

Transformation rules depend on operator ordering

Results extend to Kahler quantization of H2(T,R)

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).