The critical dimension of bosonic string theory in AdS space-time

TL;DR

This paper quantizes the bosonic string in Euclidean Anti-de Sitter space, showing it reduces to Liouville theory and determining the critical dimension as 22 using functional and graph expansion methods.

Contribution

It extends bosonic string quantization to AdS space and identifies the critical dimension as 22, incorporating the radial direction.

Findings

Critical dimension in AdS space is 22.

String reduces to Liouville theory in AdS.

Uses heat-kernel and zeta function regularisation.

Abstract

The Polyakov bosonic string is quantised in Euclidean Anti-de Sitter space-time using functional methods. Regularisation of the functional determinants using both heat-kernel and zeta function techniques shows that the AdS_{D+1} string reduces to the Liouville field theory, as in the flat space-time case. A Feynman graph expansion is used to evaluate (approximately) the coefficient multiplying the Liouville action; this then gives the critical dimension for this space-time as 22 (that is, 21 flat directions plus one radial direction).