Auxiliary tensor fields for Sp(2,R) self-duality

TL;DR

This paper extends the auxiliary tensor field formalism from U(1) to Sp(2,R) self-duality, enabling a new approach to nonlinear scalar-gauge theories with potential applications in supersymmetry.

Contribution

It generalizes the auxiliary tensor field formalism to Sp(2,R) self-duality, establishing invariance of auxiliary interactions and exploring higher-derivative extensions.

Findings

Sp(2,R) duality is equivalent to invariance of auxiliary interactions.

The formalism is derived via two different methods for robustness.

Potential applications to supersymmetric theories are discussed.

Abstract

The coset Sp(2,R)/U(1) is parametrized by two real scalar fields. We generalize the formalism of auxiliary tensor (bispinor) fields in U(1) self-dual nonlinear models of abelian gauge fields to the case of Sp(2,R) self-duality. In this new formulation, Sp(2,R) duality of the nonlinear scalar-gauge equations of motion is equivalent to an Sp(2,R) invariance of the auxiliary interaction. We derive this result in two different ways, aiming at its further application to supersymmetric theories. We also consider an extension to interactions with higher derivatives.