The critical dimension of bosonic string theory in AdS space-time
Ian Davies, Paul Mansfield
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 AdSD+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).
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