# Bosonic vertex representations of the toroidal superalgebras in type D(m,n)

## TL;DR

This paper constructs vertex representations of 2-toroidal Lie superalgebras of type D(m,n) using bosonic fields and vertex operators, advancing the understanding of their algebraic structure.

## Contribution

It introduces a novel construction of vertex representations for 2-toroidal Lie superalgebras of type D(m,n) utilizing bosonic fields and vertex operators.

## Key findings

- Constructed explicit vertex representations
- Utilized bosonic fields and vertex operators
- Enhanced understanding of algebraic structures

## Abstract

In this paper, vertex representations of the 2-toroidal Lie superalgebras of type $D(m, n)$ are constructed using both bosonic fields and vertex operators based on their loop algebraic presentation.