Determinant and Weyl anomaly of Dirac operator: a holographic derivation

Abstract

We present a holographic formula relating functional determinants: the fermion determinant in the one-loop effective action of bulk spinors in an asymptotically locally AdS background, and the determinant of the two-point function of the dual operator at the conformal boundary. The formula originates from AdS/CFT heuristics that map a quantum contribution in the bulk partition function to a subleading large-N contribution in the boundary partition function. We use this holographic picture to address questions in spectral theory and conformal geometry. As an instance, we compute the type-A Weyl anomaly and the determinant of the iterated Dirac operator on round spheres, express the latter in terms of Barnes' multiple gamma function and gain insight into a conjecture by Bär and Schopka.

11 pages; new comments and references added, typos corrected

References in corpus (5)

• Black hole determinants and quasinormal modes
• Determinants and conformal anomalies of GJMS operators on spheres
• Conformal Gravity from AdS/CFT mechanism
• Dimensional asymptotics of effective actions on S^n, and proof of Bär-Schopka's conjecture
• A Gauge-Gravity Relation in the One-loop Effective Action

Cited by in corpus (5)

• Fermions in AdS and Gross-Neveu BCFT
• On Renyi entropy for free conformal fields: holographic and q-analog recipes
• Scalar and Spinor Effective Actions in Global de Sitter
• UV-finite "old" conformal bootstrap on AdS: scalar case
• Spinor vertexes and bubbles in the "old" conformal bootstrap on AdS and FMH problem: Yukawa model