The AdS/CFT correspondence and Spectrum Generating Algebras

TL;DR

This paper explores the spectrum generating algebras in string theory and M-theory on AdS backgrounds, linking classical supergravity spectra with algebraic structures and their implications in conformal field theories.

Contribution

It identifies the spectrum generating algebras for various AdS backgrounds and discusses their role in classical supergravity and conformal field theories.

Findings

Spectrum generating algebras are identified for multiple AdS backgrounds.

Classical supergravity spectra are characterized by specific algebra representations.

Implications of these algebras in the conformal field theory context are discussed.

Abstract

We list the spectrum generating algebras for string theory and M-theory compactified on various backgrounds of the form $AdS_{d+1} \times S^n$. We identify the representations of these algebras which make up the classical supergravity spectra and argue for the presence of these spectrum generating algebras in the classical string/M-theory. We also discuss the role of the spectrum generating algebras on the conformal field theory side.