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Title: Giant Wilson loops and AdS2/dCFT1

Abstract

The 1/2-BPS Wilson loop in N = 4 supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS2 × S2 and AdS2 × S4 worldvolume geometries, ending at the AdS5 boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the ’t Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- andmore » four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.« less

Authors:
 [1];  [1];  [2]
  1. Princeton Univ., NJ (United States)
  2. Inst. for Advanced Study, Princeton, NJ (United States)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Science Foundation (NSF)
OSTI Identifier:
1737767
Grant/Contract Number:  
SC0009988; PHY-1620542; PHY-1914860
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Conformal Field Theory; D-branes; Field Theories in Higher Dimensions

Citation Formats

Giombi, Simone, Jiang, Jiaqi, and Komatsu, Shota. Giant Wilson loops and AdS2/dCFT1. United States: N. p., 2020. Web. doi:10.1007/jhep11(2020)064.
Giombi, Simone, Jiang, Jiaqi, & Komatsu, Shota. Giant Wilson loops and AdS2/dCFT1. United States. https://doi.org/10.1007/jhep11(2020)064
Giombi, Simone, Jiang, Jiaqi, and Komatsu, Shota. Fri . "Giant Wilson loops and AdS2/dCFT1". United States. https://doi.org/10.1007/jhep11(2020)064. https://www.osti.gov/servlets/purl/1737767.
@article{osti_1737767,
title = {Giant Wilson loops and AdS2/dCFT1},
author = {Giombi, Simone and Jiang, Jiaqi and Komatsu, Shota},
abstractNote = {The 1/2-BPS Wilson loop in N = 4 supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS2 × S2 and AdS2 × S4 worldvolume geometries, ending at the AdS5 boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the ’t Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.},
doi = {10.1007/jhep11(2020)064},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2020,
place = {United States},
year = {2020},
month = {11}
}

Works referenced in this record:

Semi-classical analysis of the inner product of Bethe states
journal, June 2014


2D BPS rings from sphere partition functions
journal, April 2018


All-genus calculation of Wilson loops using D-branes
journal, February 2005


Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003


Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM
text, January 2015


Toda theory in AdS2 and 𝒲An-algebra structure of boundary correlators
journal, October 2019

  • Beccaria, Matteo; Landolfi, Giulio
  • Journal of High Energy Physics, Vol. 2019, Issue 10
  • DOI: 10.1007/JHEP10(2019)003

Wilson loop average for an arbitrary contour in two-dimensional U(N) gauge theory
journal, March 1981


Exact null octagon
journal, May 2020

  • Belitsky, A. V.; Korchemsky, G. P.
  • Journal of High Energy Physics, Vol. 2020, Issue 5
  • DOI: 10.1007/JHEP05(2020)070

Boundary TBA, trees and loops
journal, December 2019


Correlation functions in the CFTd/AdSd+1 correspondence
journal, April 1999


Clustering and the three-point function
journal, October 2016

  • Jiang, Yunfeng; Komatsu, Shota; Kostov, Ivan
  • Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 45
  • DOI: 10.1088/1751-8113/49/45/454003

Integrable quantum field theory with boundaries: the exact g-function
journal, September 2004


One-loop effective action of the holographic antisymmetric Wilson loop
journal, May 2012

  • Faraggi, Alberto; Mück, Wolfgang; Pando Zayas, Leopoldo A.
  • Physical Review D, Vol. 85, Issue 10
  • DOI: 10.1103/PhysRevD.85.106015

Wilson loops in supersymmetric Yang–Mills theory
journal, August 2000


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
  • DOI: 10.1063/1.1372177

Eigenvalues and degeneracies for n ‐dimensional tensor spherical harmonics
journal, October 1984

  • Rubin, Mark A.; Ordóñez, Carlos R.
  • Journal of Mathematical Physics, Vol. 25, Issue 10
  • DOI: 10.1063/1.526034

Exact results for Wilson loops in arbitrary representations
journal, January 2014


On $ \mathcal{O}(1) $ contributions to the free energy in Bethe Ansatz systems: the exact g-function
journal, August 2010


Green-Schwarz string in AdS 5 × S 5 : semiclassical partition function
journal, March 2000


Asymptotic four point functions
journal, July 2019

  • Basso, Benjamin; Coronado, Frank; Komatsu, Shota
  • Journal of High Energy Physics, Vol. 2019, Issue 7
  • DOI: 10.1007/JHEP07(2019)082

Operators and higher genus mirror curves
journal, February 2017

  • Codesido, Santiago; Gu, Jie; Mariño, Marcos
  • Journal of High Energy Physics, Vol. 2017, Issue 2
  • DOI: 10.1007/JHEP02(2017)092

The 1/2 BPS ’t Hooft loops in $\mathcal {N}=4$ SYM as instantons in 2D Yang–Mills
journal, February 2013


Non-abelian Toda theory on AdS₂ and AdS₂/CFT₂1/2 duality
text, January 2019


Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT1
journal, August 2020

  • Bianchi, L.; Bliard, G.; Forini, V.
  • Journal of High Energy Physics, Vol. 2020, Issue 8
  • DOI: 10.1007/JHEP08(2020)143

Localization of the four-dimensional $ \mathcal{N}=4 $ SYM to a two-sphere and 1/8 BPS Wilson loops
journal, December 2012


Taming defects in $$ \mathcal{N} $$ = 4 super-Yang-Mills
journal, August 2020


Integrability of Green-Schwarz sigma models with boundaries
journal, August 2011


Wilson loops in Script N = 4 SYM and fermion droplets
journal, June 2006


Wilson Loops in Large N Field Theories
journal, June 1998


The Wilson loop CFT: insertion dimensions and structure constants from wavy lines
journal, July 2017

  • Cooke, Michael; Dekel, Amit; Drukker, Nadav
  • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 33
  • DOI: 10.1088/1751-8121/aa7db4

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

  • Maldacena, Juan
  • International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133
  • DOI: 10.1023/A:1026654312961

Graviton exchange and complete four-point functions in the AdS/CFT correspondence
journal, November 1999


A maximally supersymmetric Kondo model
journal, August 2012


Scalar insertions in cusped Wilson loops in the ladders limit of planar $$ \mathcal{N} $$ = 4 SYM
journal, May 2020


Small deformations of supersymmetric Wilson loops and open spin-chains
journal, July 2006


Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory
text, January 2019


Bootstrapping the half-BPS line defect
journal, October 2018

  • Liendo, Pedro; Meneghelli, Carlo; Mitev, Vladimir
  • Journal of High Energy Physics, Vol. 2018, Issue 10
  • DOI: 10.1007/JHEP10(2018)077

Stable wrapped branes
journal, May 2001


Determinant Formula for the Octagon Form Factor in N = 4 Supersymmetric Yang-Mills Theory
journal, June 2019


Perturbative four-point functions in planar N = 4 $$ \mathcal{N}=4 $$ SYM From hexagonalization
journal, January 2019


Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT
journal, January 2008


Topological Strings from Quantum Mechanics
journal, April 2016


Classification of extended operators in conformal field theories
journal, August 2006


Bubbling Geometries for Half-Bps Wilson Lines
journal, March 2007


Wilson loops of anti-symmetric representation and D5-branes
journal, May 2006


Correlators on non-supersymmetric Wilson line in $$ \mathcal{N}=4 $$ SYM and AdS2/CFT1
journal, May 2019

  • Beccaria, Matteo; Giombi, Simone; Tseytlin, Arkady A.
  • Journal of High Energy Physics, Vol. 2019, Issue 5
  • DOI: 10.1007/JHEP05(2019)122

Non-perturbative defect one-point functions in planar N = 4 super-Yang-Mills
journal, September 2020


Correlation functions of Coulomb branch operators
journal, January 2017

  • Gerchkovitz, Efrat; Gomis, Jaume; Ishtiaque, Nafiz
  • Journal of High Energy Physics, Vol. 2017, Issue 1
  • DOI: 10.1007/JHEP01(2017)103

Wilson loops as D 3-branes
journal, January 2007


Notes on supersymmetric Wilson loops on a two-sphere
text, January 2009


All-genus calculation of Wilson loops using D-branes
journal, February 2005


Half-BPS Wilson loop and AdS 2 /CFT 1
journal, September 2017


Quantum spectral curve for arbitrary state/operator in AdS5/CFT4
journal, September 2015

  • Gromov, Nikolay; Kazakov, Vladimir; Leurent, Sébastien
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)187

Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS7 × S4
journal, July 2020

  • Drukker, Nadav; Giombi, Simone; Tseytlin, Arkady A.
  • Journal of High Energy Physics, Vol. 2020, Issue 7
  • DOI: 10.1007/JHEP07(2020)101

A study of quantum field theories in AdS at finite coupling
journal, January 2019

  • Carmi, Dean; Di Pietro, Lorenzo; Komatsu, Shota
  • Journal of High Energy Physics, Vol. 2019, Issue 1
  • DOI: 10.1007/JHEP01(2019)200

Exact results for Wilson loops in superconformal Chern-Simons theories with matter
journal, March 2010

  • Kapustin, Anton; Willett, Brian; Yaakov, Itamar
  • Journal of High Energy Physics, Vol. 2010, Issue 3
  • DOI: 10.1007/JHEP03(2010)089

Quantum Spectral Curve for Planar N = 4 Super-Yang-Mills Theory
journal, January 2014


Correlation functions in matrix models modified by wormhole terms
journal, April 1995


Integrable quantum field theory with boundaries: the exact g-function
text, January 2004


Holographic Wilson loops
journal, August 2006


Supersymmetric Liouville theory in AdS2 and AdS/CFT
journal, November 2019

  • Beccaria, Matteo; Jiang, Hongliang; Tseytlin, Arkady A.
  • Journal of High Energy Physics, Vol. 2019, Issue 11
  • DOI: 10.1007/JHEP11(2019)051

The octagon as a determinant
journal, November 2019

  • Kostov, Ivan; Petkova, Valentina B.; Serban, Didina
  • Journal of High Energy Physics, Vol. 2019, Issue 11
  • DOI: 10.1007/JHEP11(2019)178

Integrable Wilson loops
journal, October 2013


Operator product expansion of higher rank Wilson loops from D-branes and matrix models
journal, October 2006


Gravity duals of half-BPS Wilson loops
journal, June 2007


Spectral Theory and Mirror Curves of Higher Genus
journal, October 2016


Exact Three-Point Functions of Determinant Operators in Planar N = 4 Supersymmetric Yang-Mills Theory
journal, November 2019


Bootstrapping the half-BPS line defect
text, January 2018


Half-BPS Wilson loop and AdS$_2$/CFT$_1$
text, January 2017


D5-brane boundary reflection factors
journal, May 2013

  • Correa, Diego H.; Massolo, Fidel I. Schaposnik
  • Journal of High Energy Physics, Vol. 2013, Issue 5
  • DOI: 10.1007/JHEP05(2013)095

Octagon at finite coupling
journal, July 2020

  • Belitsky, A. V.; Korchemsky, G. P.
  • Journal of High Energy Physics, Vol. 2020, Issue 7
  • DOI: 10.1007/JHEP07(2020)219

Supersymmetric Wilson loops on S 3
journal, May 2008


Correlators of supersymmetric Wilson-loops, protected operators and matrix models in 𝒩 = 4 SYM
journal, August 2009


Boundary correlators in WZW model on AdS2
journal, May 2020

  • Beccaria, Matteo; Jiang, Hongliang; Tseytlin, Arkady A.
  • Journal of High Energy Physics, Vol. 2020, Issue 5
  • DOI: 10.1007/JHEP05(2020)099

Invasion of the giant gravitons from anti-de Sitter space
journal, May 2000


Antisymmetric Wilson loops in N $$ \mathcal{N} $$ = 4 SYM beyond the planar limit
journal, January 2018


The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
journal, August 2012

  • Correa, Diego; Maldacena, Juan; Sever, Amit
  • Journal of High Energy Physics, Vol. 2012, Issue 8
  • DOI: 10.1007/JHEP08(2012)134

Giant Gravitons in Conformal Field Theory
journal, April 2002


3d $$ \mathcal{N} $$ = 4 OPE coefficients from Fermi gas
journal, July 2020

  • Chester, Shai M.; Kalloor, Rohit R.; Sharon, Adar
  • Journal of High Energy Physics, Vol. 2020, Issue 7
  • DOI: 10.1007/JHEP07(2020)041

The spectrum of excitations of holographic Wilson loops
journal, May 2011

  • Faraggi, Alberto; Pando Zayas, Leopoldo A.
  • Journal of High Energy Physics, Vol. 2011, Issue 5
  • DOI: 10.1007/JHEP05(2011)018

Excited states of one-dimensional defect CFTs from the quantum spectral curve
journal, July 2020

  • Grabner, David; Gromov, Nikolay; Julius, Julius
  • Journal of High Energy Physics, Vol. 2020, Issue 7
  • DOI: 10.1007/JHEP07(2020)042

Two-point correlators in N = 2 gauge theories
journal, January 2018


Hexagonalization of correlation functions
journal, January 2017


Functional equations and separation of variables for exact g-function
journal, September 2020


Topological holography: The example of the D2-D4 brane system
journal, January 2020


Four-point functions in the CFT-AdS correspondence
journal, March 1999


Loop equation and exact soft anomalous dimension in $$ \mathcal{N} $$ = 4 super Yang-Mills
journal, June 2020


More exact results in the Wilson loop defect CFT: bulk-defect OPE, nonplanar corrections and quantum spectral curve
journal, February 2019

  • Giombi, Simone; Komatsu, Shota
  • Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 12
  • DOI: 10.1088/1751-8121/ab046c

Boundary entropy of integrable perturbed SU (2)k WZNW
journal, August 2019

  • Vu, Dinh-Long; Kostov, Ivan; Serban, Didina
  • Journal of High Energy Physics, Vol. 2019, Issue 8
  • DOI: 10.1007/JHEP08(2019)154

On gravitational description of Wilson lines
journal, June 2006


Effective Quantum Field Theory for the Thermodynamical Bethe Ansatz
journal, February 2020


Higher rank Wilson loops from a matrix model
journal, August 2006


Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
text, January 2017


Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops
journal, May 2012


Conformal four point functions and the operator product expansion
journal, April 2001


Non-abelian Toda theory on AdS2 and $$ {\mathrm{AdS}}_2/{\mathrm{CFT}}_2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} $$ duality
journal, September 2019

  • Beccaria, Matteo; Jiang, Hongliang; Tseytlin, Arkady A.
  • Journal of High Energy Physics, Vol. 2019, Issue 9
  • DOI: 10.1007/s13130-019-11219-y