BiHermitian Supersymmetric Quantum Mechanics

TL;DR

This paper develops a supersymmetric quantum mechanics model based on biHermitian geometry, demonstrating its full supersymmetry, quantization, and connection to Hodge theory on twisted generalized Kaehler manifolds.

Contribution

It formulates and quantizes supersymmetric quantum mechanics on biHermitian target spaces, linking it to Hodge theory and broadening understanding of biHermitian topological sigma models.

Findings

Model reproduces Hodge theory for twisted generalized Kaehler manifolds

Demonstrates full supersymmetry and quantization procedure

Connects biHermitian geometry with topological sigma models

Abstract

BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.