Pseudoduality in Supersymmetric Sigma Models on Symmetric Spaces

TL;DR

This paper explores pseudoduality in supersymmetric sigma models on symmetric spaces, revealing how different methods affect the algebraic relations and constraints, especially when mixing terms are considered.

Contribution

It compares orthonormal coframe and component expansion methods, showing how mixing pseudoduality alters constraint relations in supersymmetric sigma models.

Findings

Commuting brackets become anticommuting due to Grassmann numbers.

Constraint relations are remnants of mixing pseudoduality.

Including mixing terms removes certain constraints.

Abstract

We discuss the target space pseudoduality in supersymmetric sigma models on symmetric spaces using two different methods, orthonormal coframe and component expansion. These two methods yield similar results to the classical cases with the exception that commuting bracket relations in classical case turns out to be anticommuting ones because of the appearance of grassmann numbers. In component expansion method it is understood that constraint relations in case of non-mixing pseudoduality are the remnants of mixing pseudoduality. Once mixing terms are included in the pseudoduality relations the constraint relations disappear.