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arXiv · 1111.1463

Determinant and Weyl anomaly of Dirac operator: a holographic derivation

Rodrigo Aros·Danilo E Diaz
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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 B\"ar and Schopka.

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Rodrigo Aros, Danilo E Diaz. 2011-11-07. Determinant and Weyl anomaly of Dirac operator: a holographic derivation. https://doi.org/10.1088/1751-8113/45/12/125401

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