Generalized Berezin-Toeplitz quantization of Kaehler supermanifolds

TL;DR

This paper extends Berezin-Toeplitz quantization to compact Hodge supermanifolds using super-analogues of coherent states, enabling finite supersymmetric quantum field theories on quantized supermanifolds.

Contribution

It introduces a generalized quantization framework for supermanifolds and proposes supersymmetric sigma-models with finite quantum field theories.

Findings

Quantization of affine and projective superspaces achieved.

Finite quantum field theories preserving supersymmetry constructed.

New super-analogues of Rawnsley's coherent states developed.

Abstract

We extend the construction of generalized Berezin and Berezin-Toeplitz quantization to the case of compact Hodge supermanifolds. Our approach is based on certain super-analogues of Rawnsley's coherent states. As applications, we discuss the quantization of affine and projective superspaces. Furthermore, we propose a definition of supersymmetric sigma-models on quantized Hodge supermanifolds. The corresponding quantum field theories are finite and thus yield supersymmetry-preserving regularizations for QFTs defined on flat superspace.