Superopers revisited

TL;DR

This paper explores the concept of superopers, extending the geometric Langlands correspondence to Lie superalgebras, and relates them to $qq$-systems and Bethe ansatz equations, including their $q$-deformations.

Contribution

It introduces the notion of superopers and connects them to $qq$-systems for Lie superalgebras, advancing understanding of their spectra and Bethe ansatz equations.

Findings

Superopers relate to $qq$-systems in Lie superalgebras.

The paper discusses $q$-deformations of superopers.

Connections to Bethe ansatz equations are established.

Abstract

The relation between special connections on the projective line, called Miura opers, and the spectra of integrable models of Gaudin type provides an important example of the geometric Langlands correspondence. The possible generalization of that correspondence to simple Lie superalgebras is much less studied. Recently some progress has been made in understanding the spectra of Gaudin models and the corresponding Bethe ansatz equations for some simple Lie superalgebras. At the same time, the original example was reformulated in terms of an intermediate object: Miura-Pl\"ucker oper. It has a direct relation to the so-called $qq$-systems, the functional form of Bethe ansatz, which, in particular, allows $q$-deformation. In this note, we discuss the notion of superoper and relate it to the examples of $qq$-systems for Lie superalgebras, which were recently studied in the context of Bethe ansatz equations. We also briefly discuss the $q$-deformation of these constructions.