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

Journal Article · · Journal of Physics. A, Mathematical and Theoretical
 [1];  [2]
  1. Princeton Univ., NJ (United States). Dept. of Physics; Institute for Advanced Study
  2. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
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We perform here exact computations of correlation functions of 1/2-BPS local operators and protected operator insertions on the 1/8-BPS Wilson loop in $$\mathcal{N}=4$$ SYM. This generalizes the results of our previous paper arXiv:1802.05201, which employs supersymmetric localization, OPE and the Gram-Schmidt process. In particular, we conduct a detailed analysis for the 1/2-BPS circular (or straight) Wilson loop in the planar limit, which defines an interesting nontrivial defect CFT. We compute its bulk-defect structure constants at finite 't Hooft coupling, and present simple integral expressions in terms of the $$Q$$-functions that appear in the Quantum Spectral Curve---a formalism originally introduced for the computation of the operator spectrum. The results at strong coupling are found to be in precise agreement with the holographic calculation based on perturbation theory around the AdS$$_2$$ string worldsheet, where they correspond to correlation functions of open string fluctuations and closed string vertex operators inserted on the worldsheet. Along the way, we clarify several aspects of the Gram-Schmidt analysis which were not addressed in the previous paper. Specifically, we clarify the role played by the multi-trace operators at the non-planar level, and confirm its importance by computing the non-planar correction to the defect two-point function. We also provide a formula for the first non-planar correction to the defect correlators in terms of the Quantum Spectral Curve, which suggests the potential applicability of the formalism to the non-planar correlation functions.

Research Organization:
Inst. for Advanced Study, Princeton, NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF)
Grant/Contract Number:
SC0009988
OSTI ID:
1596661
Alternate ID(s):
OSTI ID: 22985394
Journal Information:
Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 12 Vol. 52; ISSN 1751-8113
Publisher:
IOP PublishingCopyright Statement
Country of Publication:
United States
Language:
English

References (104)

Analytic solution of Bremsstrahlung TBA II: turning on the sphere angle journal October 2013
Gravity duals of half-BPS Wilson loops text January 2007
Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops text January 2009
Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS journal January 2013
Large-N correlation functions in N $$ \mathcal{N} $$ = 2 superconformal QCD journal January 2017
Correlation functions of Coulomb branch operators journal January 2017
Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects journal January 2017
Hexagonalization of correlation functions journal January 2017
Bremsstrahlung function, leading Lüscher correction at weak coupling and localization journal February 2016
Colour-dressed hexagon tessellations for correlation functions and non-planar corrections journal February 2018
Correlators of supersymmetric Wilson loops at weak and strong coupling journal March 2010
Non-supersymmetric Wilson loop in N $$ \mathcal{N} $$ = 4 SYM and defect 1d CFT journal March 2018
Correlators between Wilson loop and chiral operators in N = 2 $$ \mathcal{N}=2 $$ conformal gauge theories journal March 2018
Quantum Spectral Curve for a cusped Wilson line in N = 4 $$ \mathcal{N}=4 $$ SYM journal April 2016
A limit for large R-charge correlators in N $$ \mathcal{N} $$ = 2 theories journal May 2018
Exact correlators on the Wilson loop in N = 4 $$ \mathcal{N}=4 $$ SYM: localization, defect CFT, and integrability journal May 2018
Precision matching of circular Wilson loops and strings in AdS5 × S5 journal May 2018
Large N correlation functions in superconformal field theories journal June 2016
Notes on supersymmetric Wilson loops on a two-sphere journal July 2010
Exact Bremsstrahlung functions in ABJM theory journal July 2018
Towards the exact Bremsstrahlung function of ABJM theory journal August 2017
Scattering amplitudes — Wilson loops duality for the first non-planar correction journal August 2018
Correlators of chiral primaries and 1/8 BPS Wilson loops from perturbation theory journal September 2014
Correlators of local operators and 1/8 BPS Wilson loops on S 2 from 2d YM and matrix models journal October 2010
Analytic solution of Bremsstrahlung TBA II: turning on the sphere angle journal October 2013
Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation journal October 2017
Tessellating cushions: four-point functions in N $$ \mathcal{N} $$ = 4 SYM journal October 2017
Connected correlator of 1/2 BPS Wilson loops in N = 4 $$ \mathcal{N}=4 $$ SYM journal October 2018
Quantum spectral curve and structure constants in N = 4 $$ \mathcal{N}=4 $$ SYM: cusps in the ladder limit journal October 2018
Bootstrapping the half-BPS line defect journal October 2018
Analytic solution of Bremsstrahlung TBA journal November 2012
Structure constants of operators on the Wilson loop from integrability journal November 2017
Handling handles. Part II. Stratification and data analysis journal November 2018
Localization of the four-dimensional $ \mathcal{N}=4 $ SYM to a two-sphere and 1/8 BPS Wilson loops journal December 2012
Operator mixing in large N superconformal field theories on S4 and correlators with Wilson loops journal December 2016
Structure constants of defect changing operators on the 1/2 BPS Wilson loop journal December 2017
Phase transition of anti-symmetric Wilson loops in N = 4 $$ \mathcal{N}=4 $$ SYM journal December 2017
Spin chain integrability in non-supersymmetric Wilson loops journal December 2018
Universality of Toda equation in N=2$$ \mathcal{N}=2 $$ superconformal field theories journal February 2019
Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity journal November 2001
Wilson loops in supersymmetric Yang–Mills theory journal August 2000
More exact predictions of SUSYM for string theory journal November 2001
Wrapping interactions and the genus expansion of the 2-point function of composite operators journal September 2005
Wrapping interactions and a new source of corrections to the spin-chain/string duality journal February 2006
A semiclassical string description of Wilson loop with local operators journal July 2008
Half-BPS Wilson loop and AdS 2 /CFT 1 journal September 2017
Two-point correlators in N = 2 gauge theories journal January 2018
On non-supersymmetric generalizations of the Wilson–Maldacena loops in N = 4 SYM journal September 2018
An exact prediction of N=4 supersymmetric Yang–Mills theory for string theory journal July 2001
Green-Schwarz string in AdS 5 × S 5 : semiclassical partition function journal March 2000
A Novel Long Range Spin Chain and Planar N =4 Super Yang-Mills journal July 2004
All-genus calculation of Wilson loops using D-branes journal February 2005
Wilson loops of anti-symmetric representation and D5-branes journal May 2006
On gravitational description of Wilson lines journal June 2006
Small deformations of supersymmetric Wilson loops and open spin-chains journal July 2006
Holographic Wilson loops journal August 2006
Non-relativistic string and D-branes on AdS 5 × S 5 from semiclassical approximation journal May 2007
Gravity duals of half-BPS Wilson loops journal June 2007
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
The Wilson loop CFT: insertion dimensions and structure constants from wavy lines journal July 2017
Operator product expansion for Wilson loops and surfaces in the large N limit journal April 1999
Wilson loops and minimal surfaces journal November 1999
Open string fluctuations in AdS 5 × S 5 and operators with a large R charge journal November 2002
Wilson loops: From 4D supersymmetric Yang-Mills theory to 2D Yang-Mills theory journal February 2008
Quantum Spectral Curve for Planar N = 4 Super-Yang-Mills Theory journal January 2014
Exact Bremsstrahlung Function in N = 2 Superconformal Field Theories journal February 2016
Line Defects and Radiation in N = 2 Conformal Theories journal October 2018
Handling Handles: Nonplanar Integrability in N = 4 Supersymmetric Yang-Mills Theory journal December 2018
Wilson Loops in Large N Field Theories journal June 1998
Bubbling Geometries for Half-Bps Wilson Lines journal March 2007
Handling handles. Part II. Stratification and data analysis text January 2018
Towards the exact Bremsstrahlung function of ABJM theory text January 2017
Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation text January 2017
Bootstrapping the half-BPS line defect text January 2018
Handling handles. Part II. Stratification and data analysis text January 2018
Colour-dressed hexagon tessellations for correlation functions and non-planar corrections text January 2018
Three-point functions of chiral operators in $D = 4 , \mathcal{N} = 4$ SYM at large $N$ journal January 1998
Invariants of algebraic curves and topological expansion journal January 2007
A Semiclassical String Description of Wilson Loop with Local Operators text January 2007
Supersymmetric Wilson loops on S^3 text January 2007
Notes on supersymmetric Wilson loops on a two-sphere text January 2009
The Exact Bremsstrahlung Function in N=2 Superconformal Field Theories text January 2015
Bremsstrahlung function, leading Luscher correction at weak coupling and localization text January 2015
Operator Mixing in Large $N$ Superconformal Field Theories on $\mathbb{S}^4$ and Correlators with Wilson loops text January 2016
Bootstrap equations for $\mathcal{N}=4$ SYM with defects text January 2016
Hexagonalization of Correlation Functions text January 2016
The Wilson loop CFT: Insertion dimensions and structure constants from wavy lines text January 2017
Two-point Correlators in N=2 Gauge Theories text January 2017
Towards the exact Bremsstrahlung function of ABJM theory text January 2017
Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation text January 2017
Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop text January 2017
Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit text January 2018
Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability text January 2018
Exact Bremsstrahlung functions in ABJM theory text January 2018
Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories text January 2018
Precision matching of circular Wilson loops and strings in AdS(5)xS(5) text January 2018
Universality of Toda equation in ${\cal N}=2$ superconformal field theories text January 2018
Spin chain integrability in non-supersymmetric Wilson loops text January 2018
Green-Schwarz String in AdS_5 x S^5: Semiclassical Partition Function text January 2000
All-genus calculation of Wilson loops using D-branes text January 2005
Wrapping interactions and the genus expansion of the 2-point function of composite operators text January 2005
Bubbling Geometries for Half BPS Wilson lines text January 2006
Small deformations of supersymmetric Wilson loops and open spin-chains text January 2006

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Supersymmetric Wilson loops in two dimensions and duality journal July 2019

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AdS/CFT
conformal field theory
defect CFT
supersymmetry