Functional determinants of radial operators in AdS 2

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

Resultado de la investigación: Article

3 Citas (Scopus)

Resumen

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.

Idioma originalEnglish
Número de artículo7
PublicaciónJournal of High Energy Physics
Volumen2018
N.º6
DOI
EstadoPublished - 1 jun 2018

Huella dactilar

determinants
operators
Euclidean geometry
formalism
symmetry
geometry
scattering

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Citar esto

Aguilera-Damia, Jeremías ; Faraggi, Alberto ; Zayas, Leopoldo Pando ; Rathee, Vimal ; Silva, Guillermo A. / Functional determinants of radial operators in AdS 2. En: Journal of High Energy Physics. 2018 ; Vol. 2018, N.º 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.

En: Journal of High Energy Physics, Vol. 2018, N.º 6, 7, 01.06.2018.

Resultado de la investigación: Article

TY - JOUR

T1 - Functional determinants of radial operators in AdS 2

AU - Aguilera-Damia, Jeremías

AU - Faraggi, Alberto

AU - Zayas, Leopoldo Pando

AU - Rathee, Vimal

AU - Silva, Guillermo A.

PY - 2018/6/1

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N2 - 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.

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.

KW - 1/N Expansion

KW - AdS-CFT Correspondence

KW - Supersymmetric Gauge Theory

KW - Wilson

KW - ’t Hooft and Polyakov loops

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