Extending the non-relativistic string AdS coset

TL;DR

This paper extends the non-relativistic string algebra in AdS$_5\times$S$^5$ using Lie algebra expansion, demonstrating a non-degenerate invariant inner product and a finite-dimensional representation.

Contribution

It introduces a new extended algebra for non-relativistic strings in AdS space with a non-degenerate invariant form and finite-dimensional representation.

Findings

Extended algebra admits a non-degenerate inner product.

The algebra is invariant under the full extended algebra.

Finite-dimensional representation constructed.

Abstract

Inspired by Lie algebra expansion, we consider an extension of the algebra introduced in arXiv:2203.07386 for the non-relativistic string coset action in AdS$_5\times$S$^5$. We show that the extended algebra admits a non-degenerate inner product which is adjoint invariant under the full extended algebra. Furthermore, we provide a finite-dimensional representation of the extended algebra.