Unitary Representations of Some Infinite Dimensional Lie Algebras Motivated by String Theory on AdS_3

TL;DR

This paper explores unitary representations of infinite-dimensional Lie algebras relevant to string theory on AdS_3, introducing new free field constructions and insights into string formulation hybrids.

Contribution

It presents a novel free field construction for affine Lie algebras and suggests a hybrid string theory framework on AdS_3 involving N=4 superconformal algebra.

Findings

New free field representations for affine Lie algebras

Hints at a hybrid NSR-GS string formulation on AdS_3

Potential connections between algebra representations and string theory models

Abstract

We consider some unitary representations of infinite dimensional Lie algebras motivated by string theory on AdS_3. These include examples of two kinds: the A,D,E type affine Lie algebras and the N=4 superconformal algebra. The first presents a new construction for free field representations of affine Lie algebras. The second is of a particular physical interest because it provides some hints that a hybrid of the NSR and GS formulations for string theory on AdS_3 exists.