Functional determinants of radial operators in AdS 2

Jeremías Aguilera-Damia, Alberto Faraggi, Leopoldo Pando Zayas, Vimal Rathee, Guillermo A. Silva

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study the zeta-function regularization of functional determinants of Laplace and Dirac-type operators in two-dimensional Euclidean AdS2 space. More specifically, we consider the ratio of determinants between an operator in the presence of background fields with circular symmetry and the free operator in which the background fields are absent. By Fourier-transforming the angular dependence, one obtains an infinite number of one-dimensional radial operators, the determinants of which are easy to compute. The summation over modes is then treated with care so as to guarantee that the result coincides with the two-dimensional zeta-function formalism. The method relies on some well-known techniques to compute functional determinants using contour integrals and the construction of the Jost function from scattering theory. Our work generalizes some known results in flat space. The extension to conformal AdS2 geometries is also considered. We provide two examples, one bosonic and one fermionic, borrowed from the spectrum of fluctuations of the holographic 14 -BPS latitude Wilson loop.

Original languageEnglish
Article number7
JournalJournal of High Energy Physics
Volume2018
Issue number6
DOIs
Publication statusPublished - 1 Jun 2018

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determinants
operators
Euclidean geometry
formalism
symmetry
geometry
scattering

Keywords

  • 1/N Expansion
  • AdS-CFT Correspondence
  • Supersymmetric Gauge Theory
  • Wilson
  • ’t Hooft and Polyakov loops

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Cite this

Aguilera-Damia, Jeremías ; Faraggi, Alberto ; Zayas, Leopoldo Pando ; Rathee, Vimal ; Silva, Guillermo A. / Functional determinants of radial operators in AdS 2. In: Journal of High Energy Physics. 2018 ; Vol. 2018, No. 6.
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Functional determinants of radial operators in AdS 2. / Aguilera-Damia, Jeremías; Faraggi, Alberto; Zayas, Leopoldo Pando; Rathee, Vimal; Silva, Guillermo A.

In: Journal of High Energy Physics, Vol. 2018, No. 6, 7, 01.06.2018.

Research output: Contribution to journalArticle

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AB - We study the zeta-function regularization of functional determinants of Laplace and Dirac-type operators in two-dimensional Euclidean AdS2 space. More specifically, we consider the ratio of determinants between an operator in the presence of background fields with circular symmetry and the free operator in which the background fields are absent. By Fourier-transforming the angular dependence, one obtains an infinite number of one-dimensional radial operators, the determinants of which are easy to compute. The summation over modes is then treated with care so as to guarantee that the result coincides with the two-dimensional zeta-function formalism. The method relies on some well-known techniques to compute functional determinants using contour integrals and the construction of the Jost function from scattering theory. Our work generalizes some known results in flat space. The extension to conformal AdS2 geometries is also considered. We provide two examples, one bosonic and one fermionic, borrowed from the spectrum of fluctuations of the holographic 14 -BPS latitude Wilson loop.

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