Cluster Superalgebras and Stringy Integrals

TL;DR

This paper explores the physical applications of cluster superalgebras, focusing on a fermionic extension of the A2 cluster algebra and proposing an alternative superfield-based definition.

Contribution

It introduces a fermionic extension of the A2 cluster algebra and an alternative superfield-based framework for cluster superalgebras.

Findings

Fifteen cluster supervariables in the fermionic A2 extension

Proposed a superfield-based definition of cluster superalgebras

Explored potential physical applications of these structures

Abstract

We take some initial steps to explore physical applications of the cluster superalgebras recently defined by Ovsienko and Shapiro. Our primary example is a fermionic extension of the $A_2$ cluster algebra, having fifteen cluster supervariables instead of the usual five. We also explore an alternate definition of cluster superalgebras based on the promotion of cluster variables to superfields.