  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).
