One more class of scalar laplacian determinants connected with the quantum geometry of p-branes

Abstract

The determinants of Laplacians acting in real line bundles over manifolds of the form

$$M = T^q \prod\limits_\alpha {S^{N\alpha } \times \prod\limits_\beta {{{H^2 } \mathord{\left/ {\vphantom {{H^2 } {T_\beta ,}}} \right. \kern-\nulldelimiterspace} {T_\beta ,}}{\text{ }}T = S^1 ,\alpha = 1,...,k,\beta = 1,...,m} } $$

where S N _αis an N _α-dimensional sphere, N _α>1, and H ²/Г_β is a compact Riemannian surface of genus g _β>1, are evaluated in view of their potential importance in building the quantum geometry of p-branes with p+1=q+∑_α N _α+2m.