# Bosonic free field realization of twisted 2-toroidal Lie algebras

## TL;DR

This paper constructs a bosonic realization of twisted 2-toroidal Lie algebras of specific types using free fields, including the first realization of the twisted affine algebra D4^{(3)}.

## Contribution

It provides a new bosonic realization for twisted 2-toroidal Lie algebras based on a recent algebraic presentation, including the first for D4^{(3)}.

## Key findings

- Constructed bosonic realizations for types A_{2n-1}, A_{2n}, D_{n+1}, D_4.
- First bosonic realization of the twisted affine algebra D4^{(3)}.
- Utilized the Moody-Rao-Yokonuma-like presentation for the construction.

## Abstract

Using free fields, we construct a bosonic realization of toroidal Lie algebras of type $A_{2n-1}, A_{2n}, D_{n+1}, D_4$ which are twisted by a Dynkin diagram automorphism. This realization is based upon the recently found Moody-Rao-Yokonuma-like presentation. In particular, our construction contains the first bosonic realization of the twisted affine algebra $D_4^{(3)}$.