Supersymmetrization: AKSZ and beyond?

TL;DR

This paper explores advanced mathematical frameworks for gauge theories, extending existing formalisms like AKSZ and Q-bundles to include supersymmetric models, enhancing the theoretical understanding of these physical systems.

Contribution

It introduces multigraded generalizations of AKSZ and Q-bundles, broadening their applicability to supersymmetric gauge theories and sigma models.

Findings

Extended AKSZ formalism to multigraded settings

Generalized Q-bundles for supersymmetric theories

Compared approaches in supersymmetric sigma models

Abstract

In this paper we describe multigraded generalizations of some constructions useful for mathematical understanding of gauge theories: we perform a near-at-hand generalization of the Aleksandrov--Kontsevich--Schwarz--Zaboronsky procedure, we also extend the formalism of $Q$-bundles introduced first by A. Kotov and T. Strobl. We compare these approaches studying some supersymmetric sigma models important in theoretical physics.