Quasicomplex N=2, d=1 Supersymmetric Sigma Models

TL;DR

This paper introduces a new class of N=2 supersymmetric quantum mechanical sigma models with non-symmetric Hermitian metrics, revealing hidden N=4 supersymmetry in specific cases and relating to complex sigma models via Hamiltonian reduction.

Contribution

It develops a novel type of N=2 supersymmetric sigma models with non-symmetric metrics, connecting them to complex models and uncovering hidden supersymmetry structures.

Findings

Models are related to standard sigma models through similarity transformations.

In two dimensions, models exhibit hidden N=4 supersymmetry.

The models can be derived from complex supersymmetric sigma models via Hamiltonian reduction.

Abstract

We derive and discuss a new type of N=2 supersymmetric quantum mechanical sigma models which appear when the superfield action of the (1,2,1) multiplets is modified by adding an imaginary antisymmetric tensor to the target space metric, thus completing the latter to a non-symmetric Hermitian metric. These models are not equivalent to the standard de Rham sigma models, but are related to them through a certain special similarity transformation of the supercharges. On the other hand, they can be obtained by a Hamiltonian reduction from the complex supersymmetric N=2 sigma models built on the multiplets (2,2,0) and describing the Dolbeault complex on the manifolds with proper isometries. We study in detail the extremal two-dimensional case, when the target space metric is defined solely by the antisymmetric tensor, and show that the corresponding quantum systems reveal a hidden N=4 supersymmetry.