## 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.

Original language | English |
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Article number | 125401 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 45 |

Issue number | 12 |

DOIs | |

Publication status | Published - 30 Mar 2012 |

## ASJC Scopus subject areas

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