Functional determinants, generalized BTZ geometries and Selberg zeta function

Understand

We continue the study of a special entry in the AdS/CFT dictionary, namely a holographic formula relating the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter (ALAdS) space to a relative functional determinant of the scalar Laplacian in the bulk.

• A heuristic derivation of the formula involves a one-loop quantum effect in the bulk and the corresponding sub-leading correction at large N on the boundary.
• We presently explore a higher-dimensional version of the spinning BTZ black hole obtained as a quotient of hyperbolic space by a discrete subgroup of isometries generated by a loxodromic (or hyperbolic) element consisting of dilation (temperature) and torsion angles (spinning).
• The bulk computation is done using heat-kernel techniques and fractional calculus.