Determinant and Weyl anomaly of the Dirac operator: A holographic derivation

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16 Citations (Scopus)


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.

Original languageEnglish
Article number125401
JournalJournal of Physics A: Mathematical and Theoretical
Issue number12
Publication statusPublished - 30 Mar 2012

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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