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 original | English |
|---|---|
| Número de artículo | 7 |
| Publicación | Journal of High Energy Physics |
| Volumen | 2018 |
| N.º | 6 |
| DOI | |
| Estado | Published - 1 jun 2018 |
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ASJC Scopus subject areas
- Nuclear and High Energy Physics
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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
Y1 - 2018/6/1
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
UR - http://www.scopus.com/inward/record.url?scp=85048197782&partnerID=8YFLogxK
U2 - 10.1007/JHEP06(2018)007
DO - 10.1007/JHEP06(2018)007
M3 - Article
VL - 2018
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 6
M1 - 7
ER -