Pseudoduality and Complex Geometry in Sigma Models

TL;DR

This paper explores pseudoduality transformations in two-dimensional N=(2,2) sigma models on Kähler manifolds, revealing conditions for structure preservation and the impact of holomorphic isometries.

Contribution

It introduces a framework for pseudoduality transformations involving (anti)holomorphic maps and identifies conditions like vanishing torsion and Riemann curvature for these transformations.

Findings

Pseudoduality maps structures between target spaces via (anti)holomorphic transformations.

Vanishing torsion and Riemann curvature are necessary for pseudoduality.

Holomorphic isometries impose additional constraints on the pseudoduality process.

Abstract

We study the pseudoduality transformations in two dimensional N = (2, 2) sigma models on K\"ahler manifolds. We show that structures on the target space can be transformed into the pseudodual manifolds by means of (anti)holomorphic preserving mapping. This map requires that torsions related to individual spaces and riemann connection on pseudodual manifold must vanish. We also consider holomorphic isometries which puts additional constraints on the pseudoduality.