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Title: Structure constants in $$ \mathcal{N} $$ = 4 SYM at finite coupling as worldsheet g-function

Abstract

We develop a novel nonperturbative approach to a class of three-point functions in planar$$ \mathcal{N} $$ N = 4 SYM based on Thermodynamic Bethe Ansatz (TBA). More specifically, we study three-point functions of a non-BPS single-trace operator and two determinant operators dual to maximal Giant Graviton D-branes in AdS5×S5. They correspond to disk one-point functions on the worldsheet and admit a simpler and more powerful integrability description than the standard single-trace three-point functions. We first introduce two new methods to efficiently compute such correlators at weak coupling; one based on largeNcollective fields, which provides an example of open-closed-open duality discussed by Gopakumar, and the other based on combinatorics. The results so obtained exhibit a simple determinant structure and indicate that the correlator can be interpreted as a generalization ofg-functions in 2d QFT; an overlap between an integrable boundary state and a state corresponding to the single-trace operator. We then determine the boundary state at finite coupling using the symmetry, the crossing equation and the boundary Yang-Baxter equation. With the resulting boundary state, we derive the ground-stateg-function based on TBA and conjecture its generalization to other states. This is the first fully nonperturbative proposal for the structure constants of operators of finite length. The results are tested extensively at weak and strong couplings. Finally, we point out that determinant operators can provide better probes of sub-AdS locality than single-trace operators and discuss possible applications.

Authors:
 [1];  [2];  [3]
+ Show Author Affiliations
  1. European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theoretical Physics Dept.
  2. Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
  3. Imperial College, London (United Kingdom). The Blackett Lab.
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1801981
Grant/Contract Number:  
SC0009988
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: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats

Jiang, Yunfeng, Komatsu, Shota, and Vescovi, Edoardo. Structure constants in $ \mathcal{N} $ = 4 SYM at finite coupling as worldsheet g-function. United States: N. p., 2020. Web. doi:10.1007/jhep07(2020)037.
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Jiang, Yunfeng, Komatsu, Shota, & Vescovi, Edoardo. Structure constants in $ \mathcal{N} $ = 4 SYM at finite coupling as worldsheet g-function. United States. https://doi.org/10.1007/jhep07(2020)037
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Jiang, Yunfeng, Komatsu, Shota, and Vescovi, Edoardo. Mon . "Structure constants in $ \mathcal{N} $ = 4 SYM at finite coupling as worldsheet g-function". United States. https://doi.org/10.1007/jhep07(2020)037. https://www.osti.gov/servlets/purl/1801981.
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@article{osti_1801981,
title = {Structure constants in $ \mathcal{N} $ = 4 SYM at finite coupling as worldsheet g-function},
author = {Jiang, Yunfeng and Komatsu, Shota and Vescovi, Edoardo},
abstractNote = {We develop a novel nonperturbative approach to a class of three-point functions in planar$ \mathcal{N} $N= 4 SYM based on Thermodynamic Bethe Ansatz (TBA). More specifically, we study three-point functions of a non-BPS single-trace operator and two determinant operators dual to maximal Giant Graviton D-branes in AdS5×S5. They correspond to disk one-point functions on the worldsheet and admit a simpler and more powerful integrability description than the standard single-trace three-point functions. We first introduce two new methods to efficiently compute such correlators at weak coupling; one based on largeNcollective fields, which provides an example of open-closed-open duality discussed by Gopakumar, and the other based on combinatorics. The results so obtained exhibit a simple determinant structure and indicate that the correlator can be interpreted as a generalization ofg-functions in 2d QFT; an overlap between an integrable boundary state and a state corresponding to the single-trace operator. We then determine the boundary state at finite coupling using the symmetry, the crossing equation and the boundary Yang-Baxter equation. With the resulting boundary state, we derive the ground-stateg-function based on TBA and conjecture its generalization to other states. This is the first fully nonperturbative proposal for the structure constants of operators of finite length. The results are tested extensively at weak and strong couplings. Finally, we point out that determinant operators can provide better probes of sub-AdS locality than single-trace operators and discuss possible applications.},
doi = {10.1007/jhep07(2020)037},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2020,
place = {United States},
year = {Mon Jul 06 00:00:00 EDT 2020},
month = {Mon Jul 06 00:00:00 EDT 2020}
}
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  • DOI: 10.1007/s11005-010-0438-9

Quantum mechanics of null polygonal Wilson loops
journal, May 2014

The baryon propagator in terms of mesonic amplitudes
journal, September 1982

Exact results in supersymmetric field theories on manifolds with boundaries
journal, November 2013

  • Sugishita, Sotaro; Terashima, Seiji
  • Journal of High Energy Physics, Vol. 2013, Issue 11
  • DOI: 10.1007/JHEP11(2013)021

Disorder Operators in Chern-Simons-Fermion Theories
text, January 2015

Y -system for scattering amplitudes
journal, November 2010

  • Alday, Luis F.; Maldacena, Juan; Sever, Amit
  • Journal of Physics A: Mathematical and Theoretical, Vol. 43, Issue 48
  • DOI: 10.1088/1751-8113/43/48/485401

The analytic Bethe ansatz for a chain with centrally extended symmetry
journal, January 2007

One-point functions in defect CFT and integrability
journal, August 2015

  • de Leeuw, Marius; Kristjansen, Charlotte; Zarembo, Konstantin
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)098

D-brane probes in the matrix model
journal, March 2014

A planar diagram theory for strong interactions
journal, April 1974

Diagonalisation d'une classe d'hamiltoniens de spin
journal, January 1976

Holographic correlation functions for open strings and branes
journal, June 2011

  • Bak, Dongsu; Chen, Bin; Wu, Jun-Bao
  • Journal of High Energy Physics, Vol. 2011, Issue 6
  • DOI: 10.1007/JHEP06(2011)014

Supersymmetric quantum mechanics of the flux tube
journal, December 2016

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

Exact g-function flow between conformal field theories
journal, August 2010

Basso-Dixon correlators in two-dimensional fishnet CFT
journal, April 2019

  • Derkachov, Sergei; Kazakov, Vladimir; Olivucci, Enrico
  • Journal of High Energy Physics, Vol. 2019, Issue 4
  • DOI: 10.1007/JHEP04(2019)032

Integrable open spin chains from giant gravitons
journal, June 2005

Can Topology and Geometry be Measured by an Operator Measurement in Quantum Gravity?
journal, June 2017

Three-point functions in the SU(2) sector at strong coupling
journal, March 2014

Flavour singlets in gauge theory as permutations
journal, December 2016

  • Kimura, Yusuke; Ramgoolam, Sanjaye; Suzuki, Ryo
  • Journal of High Energy Physics, Vol. 2016, Issue 12
  • DOI: 10.1007/JHEP12(2016)142

Review of AdS/CFT Integrability, Chapter III.3: The Dressing Factor
journal, May 2011

AdS/dCFT one-point functions of the SU(3) sector
journal, December 2016

Giant gravitons—with strings attached (I)
journal, June 2007

AdS/dCFT one-point functions of the SU(3) sector
text, January 2016

χ-systems for correlation functions
journal, January 2019

Baryons, monopoles and dualities in Chern-Simons-matter theories
journal, February 2016

What is an integrable quench?
journal, December 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

Hexagons and correlators in the fishnet theory
journal, November 2019

  • Basso, Benjamin; Caetano, João; Fleury, Thiago
  • Journal of High Energy Physics, Vol. 2019, Issue 11
  • DOI: 10.1007/JHEP11(2019)172

Giant gravitons and correlators
journal, December 2012

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

Structure constants at wrapping order
journal, May 2017

  • Basso, Benjamin; Gonçalves, Vasco; Komatsu, Shota
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)124

New construction of eigenstates and separation of variables for SU(N) quantum spin chains
journal, September 2017

  • Gromov, Nikolay; Levkovich-Maslyuk, Fedor; Sizov, Grigory
  • Journal of High Energy Physics, Vol. 2017, Issue 9
  • DOI: 10.1007/JHEP09(2017)111

BMN correlators and operator mixing in super-Yang–Mills theory
journal, February 2003

Exploring the mirror TBA
journal, May 2010

  • Arutyunov, Gleb; Frolov, Sergey; Suzuki, Ryo
  • Journal of High Energy Physics, Vol. 2010, Issue 5
  • DOI: 10.1007/JHEP05(2010)031

Giant gravitons: A collective coordinate approach
journal, June 2013

Uncolored random tensors, melon diagrams, and the Sachdev-Ye-Kitaev models
journal, February 2017

Ramond-Ramond couplings of D-branes
journal, March 2015

  • Hashimoto, Koji; Sugishita, Sotaro; Terashima, Seiji
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/jhep03(2015)077

Baryons in the expansion
journal, November 1979

Asymptotic One-Point Functions in Gauge-String Duality with Defects
journal, December 2017

Gluing hexagons at three loops
journal, June 2016

Non-perturbative string theory from AdS/CFT
journal, February 2019

  • de Mello Koch, Robert; Gandote, Eunice; Huang, Jia-Hui
  • Journal of High Energy Physics, Vol. 2019, Issue 2
  • DOI: 10.1007/JHEP02(2019)169

S matrix of the supersymmetric nonlinear σ model
journal, April 1978

A New Supersymmetric Index
text, January 1992

Boundary Entropy of One-Dimensional Quantum Systems at Low Temperature
journal, July 2004

Non-commutative geometry and string field theory
journal, May 1986

Exact correlators of giant gravitons from dual $N = 4$ SYM theory
journal, January 2001

  • Corley, Steve; Jevicki, Antal; Ramgoolam, Sanjaye
  • Advances in Theoretical and Mathematical Physics, Vol. 5, Issue 4
  • DOI: 10.4310/ATMP.2001.v5.n4.a6

A study of open strings ending on giant gravitons, spin chains and integrability
journal, September 2006

  • Berenstein, David; Correa, Diego H.; Vázquez, Samuel E.
  • Journal of High Energy Physics, Vol. 2006, Issue 09
  • DOI: 10.1088/1126-6708/2006/09/065

The spectrum of tachyons in AdS/CFT
journal, March 2014

  • Bajnok, Zoltán; Drukker, Nadav; Hegedűs, Árpád
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/jhep03(2014)055

The structure of n -point functions of chiral primary operators in 𝒩 = 4 super Yang-Mills at one-loop
journal, April 2009

Non-analytic behavior of the Loschmidt echo in XXZ spin chains: Exact results
journal, August 2018

Gauge Theories, D-Branes and Holography
text, January 2013

Universality of long-distance AdS physics from the CFT bootstrap
journal, August 2014

  • Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.
  • Journal of High Energy Physics, Vol. 2014, Issue 8
  • DOI: 10.1007/JHEP08(2014)145

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

The complete one-loop dilatation operator of super-Yang–Mills theory
journal, January 2004

RG stability of integrable fishnet models
journal, June 2017

Tessellating cushions: four-point functions in N $$ \mathcal{N} $$ = 4 SYM
journal, October 2017

  • Eden, Burkhard; Sfondrini, Alessandro
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)098

A quantum check of AdS/dCFT
journal, January 2017

  • Buhl-Mortensen, Isak; de Leeuw, Marius; Ipsen, Asger C.
  • Journal of High Energy Physics, Vol. 2017, Issue 1
  • DOI: 10.1007/JHEP01(2017)098

A Gaudin-like determinant for overlaps of Néel and XXZ Bethe states
journal, March 2014

Weakly renormalized near 1/16 SUSY Fermi liquid operators in 𝒩 = 4 SYM
journal, October 2008

Observables of String Field Theory
journal, January 2002

Calculation of norms of Bethe wave functions
journal, September 1982

  • Korepin, V. E.
  • Communications in Mathematical Physics, Vol. 86, Issue 3
  • DOI: 10.1007/BF01212176

The full spectrum of AdS5/CFT4 I: representation theory and one-loop Q-system
journal, March 2018

  • Marboe, Christian; Volin, Dmytro
  • Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 16
  • DOI: 10.1088/1751-8121/aab34a

Disorder operators in Chern-Simons-fermion theories
journal, March 2016

One-Loop One-Point Functions in Gauge-Gravity Dualities with Defects
journal, November 2016

Shape and holography: studies of dual operators to giant gravitons
journal, December 2003

Diagonalisation d'une classe d'hamiltoniens de spin
journal, January 1976

The g-theorem and quantum information theory
journal, October 2016

  • Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo
  • Journal of High Energy Physics, Vol. 2016, Issue 10
  • DOI: 10.1007/jhep10(2016)140

Classical integrability for three-point functions: cognate structure at weak and strong couplings
journal, October 2016

  • Kazama, Yoichi; Komatsu, Shota; Nishimura, Takuya
  • Journal of High Energy Physics, Vol. 2016, Issue 10
  • DOI: 10.1007/JHEP10(2016)042

Erratum to: Exact correlators on the Wilson loop in N $$ \mathcal{N} $$ = 4 SYM: localization, defect CFT, and integrability
journal, November 2018

Integrable Matrix Product States from boundary integrability
journal, January 2019

Correlation functions of three heavy operators - the AdS contribution
text, January 2011

From large N nonplanar anomalous dimensions to open spring theory
journal, May 2012

Characteristic Polynomials of Random Matrices
journal, October 2000

  • Brézin, Edouard; Hikami, Shinobu
  • Communications in Mathematical Physics, Vol. 214, Issue 1
  • DOI: 10.1007/s002200000256

Open spin chains in super Yang-Mills at higher loops: some potential problems with integrability
journal, August 2006

Nonplanar integrability
journal, March 2011

  • Carlson, Warren; de Mello Koch, Robert; Lin, Hai
  • Journal of High Energy Physics, Vol. 2011, Issue 3
  • DOI: 10.1007/JHEP03(2011)105

The hexagon in the mirror: the three-point function in the SoV representation
journal, March 2016

  • Jiang, Yunfeng; Komatsu, Shota; Kostov, Ivan
  • Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 17
  • DOI: 10.1088/1751-8113/49/17/174007

The closed string tadpole in open string field theory
journal, August 2008

Bethe ansatz for an AdS/CFT open spin chain with non-diagonal boundaries
journal, October 2015

  • Zhang, Xin; Cao, Junpeng; Cui, Shuai
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)133

Chiral limit of N $$ \mathcal{N} $$ = 4 SYM and ABJM and integrable Feynman graphs
journal, March 2018

  • Caetano, João; Gürdoğan, Ömer; Kazakov, Vladimir
  • Journal of High Energy Physics, Vol. 2018, Issue 3
  • DOI: 10.1007/JHEP03(2018)077

The baryon propagator in terms of mesonic amplitudes
journal, September 1982

Surprisingly simple spectra
journal, February 2011

  • De Comarmond, Vincent; de Mello Koch, Robert; Jefferies, Katherine
  • Journal of High Energy Physics, Vol. 2011, Issue 2
  • DOI: 10.1007/JHEP02(2011)006
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