### 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. 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 14 -BPS latitude Wilson loop.

Original language | English |
---|---|

Article number | 7 |

Journal | Journal of High Energy Physics |

Volume | 2018 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Jun 2018 |

### Fingerprint

### 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

_{2}.

*Journal of High Energy Physics*,

*2018*(6), [7]. https://doi.org/10.1007/JHEP06(2018)007

}

_{2}',

*Journal of High Energy Physics*, vol. 2018, no. 6, 7. https://doi.org/10.1007/JHEP06(2018)007

**Functional determinants of radial operators in AdS _{2}.** / Aguilera-Damia, Jeremías; Faraggi, Alberto; Zayas, Leopoldo Pando; Rathee, Vimal; Silva, Guillermo A.

Research output: Contribution to journal › 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 -

_{2}. Journal of High Energy Physics. 2018 Jun 1;2018(6). 7. https://doi.org/10.1007/JHEP06(2018)007