Functional determinants of radial operators in AdS _{2}
We study the zetafunction regularization of functional determinants of Laplace and Diractype operators in twodimensional Euclidean AdS _{2} 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 Fouriertransforming the angular dependence, one obtains an infinite number of onedimensional 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 twodimensional zetafunction formalism. The method relies on some wellknown techniques to compute functional determinants using contour integrals and the construction of the Jost function from scattering theory. Here, our work generalizes some known results in flat space. The extension to conformal AdS _{2} geometries is also considered. We provide two examples, one bosonic and one fermionic, borrowed from the spectrum of fluctuations of the holographic 1/4BPS latitude Wilson loop.
 Authors:

^{[1]};
^{[2]};
^{[3]}
;
^{[4]}
;
^{[5]}
 Inst. de Fisica de La Plata, La Plata (Argentina). CONICET & Dept. de Fisica
 Univ. Andres Bello, Santiago (Chile). Dept. de Ciencias Fisicas, Facultad de Ciencias Exactas
 Univ. of Michigan, Ann Arbor, MI (United States). Leinweber Center for Theoretical Physics; Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
 Univ. of Michigan, Ann Arbor, MI (United States). Leinweber Center for Theoretical Physics
 Inst. de Fisica de La Plata, La Plata (Argentina). CONICET & Dept. de Fisica; Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
 Publication Date:
 Grant/Contract Number:
 SC0017808
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 6; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Univ. of Michigan, Ann Arbor, MI (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS
 OSTI Identifier:
 1457336
AguileraDamia, Jeremias, Faraggi, Alberto, Zayas, Leopoldo Pando, Rathee, Vimal, and Silva, Guillermo A. Functional determinants of radial operators in AdS2. United States: N. p.,
Web. doi:10.1007/JHEP06(2018)007.
AguileraDamia, Jeremias, Faraggi, Alberto, Zayas, Leopoldo Pando, Rathee, Vimal, & Silva, Guillermo A. Functional determinants of radial operators in AdS2. United States. doi:10.1007/JHEP06(2018)007.
AguileraDamia, Jeremias, Faraggi, Alberto, Zayas, Leopoldo Pando, Rathee, Vimal, and Silva, Guillermo A. 2018.
"Functional determinants of radial operators in AdS2". United States.
doi:10.1007/JHEP06(2018)007. https://www.osti.gov/servlets/purl/1457336.
@article{osti_1457336,
title = {Functional determinants of radial operators in AdS2},
author = {AguileraDamia, Jeremias and Faraggi, Alberto and Zayas, Leopoldo Pando and Rathee, Vimal and Silva, Guillermo A.},
abstractNote = {We study the zetafunction regularization of functional determinants of Laplace and Diractype operators in twodimensional 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 Fouriertransforming the angular dependence, one obtains an infinite number of onedimensional 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 twodimensional zetafunction formalism. The method relies on some wellknown techniques to compute functional determinants using contour integrals and the construction of the Jost function from scattering theory. Here, 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 1/4BPS latitude Wilson loop.},
doi = {10.1007/JHEP06(2018)007},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2018,
place = {United States},
year = {2018},
month = {6}
}