# Functional determinants of radial operators in AdS _{2}

## Abstract

We study the zeta-function regularization of functional determinants of Laplace and Dirac-type operators in two-dimensional 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 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. 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 1/4-BPS latitude Wilson loop.

- Authors:

- 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:

- Research Org.:
- Univ. of Michigan, Ann Arbor, MI (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1457336

- Grant/Contract Number:
- SC0017808

- Resource Type:
- Journal Article: 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 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS

### Citation Formats

```
Aguilera-Damia, Jeremias, Faraggi, Alberto, Zayas, Leopoldo Pando, Rathee, Vimal, and Silva, Guillermo A.
```*Functional determinants of radial operators in AdS2*. United States: N. p., 2018.
Web. doi:10.1007/JHEP06(2018)007.

```
Aguilera-Damia, 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.

```
Aguilera-Damia, Jeremias, Faraggi, Alberto, Zayas, Leopoldo Pando, Rathee, Vimal, and Silva, Guillermo A. Fri .
"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 = {Aguilera-Damia, Jeremias and Faraggi, Alberto and Zayas, Leopoldo Pando and Rathee, Vimal and Silva, Guillermo A.},

abstractNote = {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. 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 1/4-BPS latitude Wilson loop.},

doi = {10.1007/JHEP06(2018)007},

journal = {Journal of High Energy Physics (Online)},

number = 6,

volume = 2018,

place = {United States},

year = {Fri Jun 01 00:00:00 EDT 2018},

month = {Fri Jun 01 00:00:00 EDT 2018}

}