Vertex representations of toroidal special linear Lie superalgebras

TL;DR

This paper constructs free field representations of 2-toroidal Lie superalgebras of type A(m, n) using vertex operators and bosonic fields, based on their loop-algebraic presentation.

Contribution

It introduces a novel free field representation framework for 2-toroidal Lie superalgebras of type A(m, n).

Findings

Successful construction of free field representations.

Use of vertex operators and bosonic fields.

Foundation for further algebraic and representation theory studies.

Abstract

Based on the loop-algebraic presentation of 2-toroidal Lie superalgebras, free field representation of toroidal Lie superalgebras of type $A(m, n)$ is constructed using both vertex operators and bosonic fields.