Toroidal Lie superalgebras and free field representations

TL;DR

This paper presents a loop-algebraic framework for toroidal Lie superalgebras of classical types and constructs free field realizations for various types, advancing the understanding of their structure and representations.

Contribution

It introduces a loop-algebraic presentation for toroidal Lie superalgebras and constructs explicit free field realizations for types A, B, C, and D.

Findings

Loop-algebraic presentation for toroidal Lie superalgebras established

Explicit free field realizations constructed for types A, B, C, D

Framework facilitates further study of representations of these superalgebras

Abstract

A loop-algebraic presentation is given for toroidal Lie superalgebras of classical types. Based on the loop superalgebra presentation free field realizations of toroidal Lie superalgebras are constructed for types $A(m,n)$, $B(m,n)$, C(n) and $D(m,n)$.