Functional determinants on Mandelstam diagrams (Q915209)

The properties of Mandelstam metrics in regard to changing weights in path integrals and relations between determinants of different spins are investigated. These relations are considered in the spirit of Witten's arguments for multiplicative Ward identities. The conformal anomaly is fundamental since the path integrals over fields of different spins appear in the model. It is shown that the reparametrization invariant regularization of the Liouville action develops a Weyl anomaly at each zero of the Mandelstam metric. Elimination of the Weyl anomaly leads to equivalence with Sonode's coordinate-dependent regularization. For spin 1/2 the determinants of zero modes are finite and one obtains a genuine notion of determinants for Laplacians on spinors with respect to Mandelstam metrics.