# Zeta-function regularization of holographic Wilson loops

## Abstract

Using $${\zeta}$$-function regularization, we study the one-loop effective action of fundamental strings in $$Ad{S}_{5}\times{}{S}^{5}$$ dual to the latitude $$\frac{1}{4}$$-BPS Wilson loop in $$\mathcal{N}=4$$ super-Yang-Mills theory. To avoid certain ambiguities inherent to string theory on curved backgrounds we subtract the effective action of the holographic $$\frac{1}{2}$$-BPS Wilson loop. We find agreement with the expected field theory result at first order in the small latitude angle expansion but discrepancies at higher order.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Michigan, Ann Arbor, MI (United States); Andrés Bello National Univ., Santiago (Chile); National Univ. of La Plata (UNLP) (Argentina)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Fund for Scientific and Technological Development (FONDECYT) (Chile); National Scientific and Technical Research Council (CONICET) (Argentina)

- OSTI Identifier:
- 1464301

- Alternate Identifier(s):
- OSTI ID: 1503839

- Grant/Contract Number:
- SC0017808; 1160282; PICT 2012-0417; PIP0595/13; X648UNLP; PIP 0681

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 4; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; gauge-gravity dualities; large-N expansion in field theory; strings & branes

### Citation Formats

```
Aguilera-Damia, Jeremías, Faraggi, Alberto, Pando Zayas, Leopoldo A., Rathee, Vimal, and Silva, Guillermo A. Zeta-function regularization of holographic Wilson loops. United States: N. p., 2018.
Web. doi:10.1103/PhysRevD.98.046011.
```

```
Aguilera-Damia, Jeremías, Faraggi, Alberto, Pando Zayas, Leopoldo A., Rathee, Vimal, & Silva, Guillermo A. Zeta-function regularization of holographic Wilson loops. United States. doi:10.1103/PhysRevD.98.046011.
```

```
Aguilera-Damia, Jeremías, Faraggi, Alberto, Pando Zayas, Leopoldo A., Rathee, Vimal, and Silva, Guillermo A. Mon .
"Zeta-function regularization of holographic Wilson loops". United States. doi:10.1103/PhysRevD.98.046011.
```

```
@article{osti_1464301,
```

title = {Zeta-function regularization of holographic Wilson loops},

author = {Aguilera-Damia, Jeremías and Faraggi, Alberto and Pando Zayas, Leopoldo A. and Rathee, Vimal and Silva, Guillermo A.},

abstractNote = {Using ${\zeta}$-function regularization, we study the one-loop effective action of fundamental strings in $Ad{S}_{5}\times{}{S}^{5}$ dual to the latitude $\frac{1}{4}$-BPS Wilson loop in $\mathcal{N}=4$ super-Yang-Mills theory. To avoid certain ambiguities inherent to string theory on curved backgrounds we subtract the effective action of the holographic $\frac{1}{2}$-BPS Wilson loop. We find agreement with the expected field theory result at first order in the small latitude angle expansion but discrepancies at higher order.},

doi = {10.1103/PhysRevD.98.046011},

journal = {Physical Review D},

number = 4,

volume = 98,

place = {United States},

year = {2018},

month = {8}

}

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DOI: 10.1103/PhysRevD.98.046011

DOI: 10.1103/PhysRevD.98.046011

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Cited by: 1 work

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Works referenced in this record:

##
Instantons of two-dimensional fermionic effective actions by inverse scattering transformation

journal, September 1985

- Avan, J.; de Vega, H. J.
- Communications in Mathematical Physics, Vol. 102, Issue 3

##
Zeta function regularization of path integrals in curved spacetime

journal, June 1977

- Hawking, S. W.
- Communications in Mathematical Physics, Vol. 55, Issue 2

##
1/4 BPS circular loops, unstable world-sheet instantons and the matrix model

journal, September 2006

- Drukker, Nadav
- Journal of High Energy Physics, Vol. 2006, Issue 09

##
On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces

journal, September 1996

- Camporesi, Roberto; Higuchi, Atsushi
- Journal of Geometry and Physics, Vol. 20, Issue 1

##
Wilson Loops in Large $\mathit{N}$ Field Theories

journal, June 1998

- Maldacena, Juan
- Physical Review Letters, Vol. 80, Issue 22

##
Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in AdS 5 × S 5

journal, March 2017

- Forini, V.; Tseytlin, A. A.; Vescovi, E.
- Journal of High Energy Physics, Vol. 2017, Issue 3

##
Effective Lagrangian and energy-momentum tensor in de Sitter space

journal, June 1976

- Dowker, J. S.; Critchley, Raymond
- Physical Review D, Vol. 13, Issue 12

##
Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM

journal, March 2015

- Aguilera-Damia, Jeremías; Correa, Diego H.; Silva, Guillermo A.
- Journal of High Energy Physics, Vol. 2015, Issue 3

##
$1/N$ correction in the D3-brane description of a circular Wilson loop at strong coupling

journal, June 2014

- Buchbinder, E. I.; Tseytlin, A. A.
- Physical Review D, Vol. 89, Issue 12

##
Wilson loops in supersymmetric Yang–Mills theory

journal, August 2000

- Erickson, J. K.; Semenoff, G. W.; Zarembo, K.
- Nuclear Physics B, Vol. 582, Issue 1-3

##
An exact prediction of N=4 supersymmetric Yang–Mills theory for string theory

journal, July 2001

- Drukker, Nadav; Gross, David J.
- Journal of Mathematical Physics, Vol. 42, Issue 7

##
Precision calculation of 1/4-BPS Wilson loops in AdS5×S5

journal, February 2016

- Forini, V.; Puletti, V. Giangreco M.; Griguolo, L.
- Journal of High Energy Physics, Vol. 2016, Issue 2

##
Functional determinants for radial operators

journal, September 2006

- Dunne, Gerald V.; Kirsten, Klaus
- Journal of Physics A: Mathematical and General, Vol. 39, Issue 38

##
Functional determinants of radial operators in AdS2

journal, June 2018

- Aguilera-Damia, Jeremías; Faraggi, Alberto; Zayas, Leopoldo Pando
- Journal of High Energy Physics, Vol. 2018, Issue 6

##
Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity

journal, November 2001

- Rey, S. -J.; Yee, J. -T.
- The European Physical Journal C, Vol. 22, Issue 2

##
Green-Schwarz string in *AdS* _{5} × *S* ^{5} : semiclassical partition function

journal, March 2000

- Drukker, Nadav; Gross, David J.; Tseytlin, Arkady A.
- Journal of High Energy Physics, Vol. 2000, Issue 04

##
Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling

journal, May 2008

- Kruczenski, M.; Tirziu, A.
- Journal of High Energy Physics, Vol. 2008, Issue 05

##
Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops

journal, May 2012

- Pestun, Vasily
- Communications in Mathematical Physics, Vol. 313, Issue 1

##
Toward precision holography with supersymmetric Wilson loops

journal, April 2016

- Faraggi, Alberto; Pando Zayas, Leopoldo A.; Silva, Guillermo A.
- Journal of High Energy Physics, Vol. 2016, Issue 4

##
Spectral functions and zeta functions in hyperbolic spaces

journal, August 1994

- Camporesi, Roberto; Higuchi, Atsushi
- Journal of Mathematical Physics, Vol. 35, Issue 8

##
Supersymmetric Wilson loops on *S* ^{3}

journal, May 2008

- Drukker, Nadav; Giombi, Simone; Ricci, Riccardo
- Journal of High Energy Physics, Vol. 2008, Issue 05

##
Wilson loops: From 4D supersymmetric Yang-Mills theory to 2D Yang-Mills theory

journal, February 2008

- Drukker, Nadav; Giombi, Simone; Ricci, Riccardo
- Physical Review D, Vol. 77, Issue 4