A study of quantum field theories in AdS at finite coupling

Carmi, Dean; Di Pietro, Lorenzo; Komatsu, Shota

doi:10.1007/JHEP01(2019)200

Title: A study of quantum field theories in AdS at finite coupling

Abstract

We study the $O(N)$ and Gross-Neveu models at large $$N$$ on AdS$$_{d+1}$$ background. Thanks to the isometries of AdS, the observables in these theories are constrained by the SO$(d,2)$ conformal group even in the presence of mass deformations, as was discussed by Callan and Wilczek, and provide an interesting two-parameter family of quantities which interpolate between the S-matrices in flat space and the correlators in CFT with a boundary. For the actual computation, we judiciously use the spectral representation to resum loop diagrams in the bulk. After the resummation, the AdS $$4$$-particle scattering amplitude is given in terms of a single unknown function of the spectral parameter. We then "bootstrap" the unknown function by requiring the absence of double-trace operators in the boundary OPE. Our results are at leading nontrivial order in $$\frac{1}{N}$$, and include the full dependence on the quartic coupling, the mass parameters, and the AdS radius. In the bosonic $O(N)$ model we study both the massive phase and the symmetry-breaking phase, which exists even in AdS$$_2$$ evading Coleman's theorem, and identify the AdS analogue of a resonance in flat space. We then propose that symmetry breaking in AdS implies the existence of a conformal manifold in the boundary conformal theory. We also provide evidence for the existence of a critical point with bulk conformal symmetry, matching existing results and finding new ones for the conformal boundary conditions of the critical theories. For the Gross-Neveu model we find a bound state, which interpolates between the familiar bound state in flat space and the displacement operator at the critical point.

Authors:

Carmi, Dean ^[1]; Di Pietro, Lorenzo ^[2]; Komatsu, Shota ^[3]

California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

Publication Date:: Fri Jan 25 00:00:00 EST 2019

Research Org.:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

Contributing Org.:: Perimeter Institute for Theoretical Physics

OSTI Identifier:: 1596660

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: 2019; Journal Issue: 1; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N Expansion; Conformal Field Theory; Renormalization Group; Resummation

Citation Formats


                    Carmi, Dean, Di Pietro, Lorenzo, and Komatsu, Shota. A study of quantum field theories in AdS at finite coupling.  United States: N. p., 2019. 
Web.  doi:10.1007/JHEP01(2019)200.

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                    Carmi, Dean, Di Pietro, Lorenzo, & Komatsu, Shota. A study of quantum field theories in AdS at finite coupling.  United States.  https://doi.org/10.1007/JHEP01(2019)200

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                    Carmi, Dean, Di Pietro, Lorenzo, and Komatsu, Shota. Fri .  
"A study of quantum field theories in AdS at finite coupling".  United States.  https://doi.org/10.1007/JHEP01(2019)200.  https://www.osti.gov/servlets/purl/1596660.

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@article{osti_1596660,

  title        = {A study of quantum field theories in AdS at finite coupling},

  author       = {Carmi, Dean and Di Pietro, Lorenzo and Komatsu, Shota},

  abstractNote = {We study the $O(N)$ and Gross-Neveu models at large $N$ on AdS$_{d+1}$ background. Thanks to the isometries of AdS, the observables in these theories are constrained by the SO$(d,2)$ conformal group even in the presence of mass deformations, as was discussed by Callan and Wilczek, and provide an interesting two-parameter family of quantities which interpolate between the S-matrices in flat space and the correlators in CFT with a boundary. For the actual computation, we judiciously use the spectral representation to resum loop diagrams in the bulk. After the resummation, the AdS $4$-particle scattering amplitude is given in terms of a single unknown function of the spectral parameter. We then "bootstrap" the unknown function by requiring the absence of double-trace operators in the boundary OPE. Our results are at leading nontrivial order in $\frac{1}{N}$, and include the full dependence on the quartic coupling, the mass parameters, and the AdS radius. In the bosonic $O(N)$ model we study both the massive phase and the symmetry-breaking phase, which exists even in AdS$_2$ evading Coleman's theorem, and identify the AdS analogue of a resonance in flat space. We then propose that symmetry breaking in AdS implies the existence of a conformal manifold in the boundary conformal theory. We also provide evidence for the existence of a critical point with bulk conformal symmetry, matching existing results and finding new ones for the conformal boundary conditions of the critical theories. For the Gross-Neveu model we find a bound state, which interpolates between the familiar bound state in flat space and the displacement operator at the critical point.},

  doi          = {10.1007/JHEP01(2019)200},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 1,

  volume       = 2019,

  place        = {United States},

  year         = {Fri Jan 25 00:00:00 EST 2019},

  month        = {Fri Jan 25 00:00:00 EST 2019}

}

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Nishida, Mitsuhiro; Tamaoka, Kotaro
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DOI: 10.48550/arxiv.1805.00217

Analytic Bootstrap for Boundary CFT
text, January 2018

Bissi, Agnese; Hansen, Tobias; Söderberg, Alexander
arXiv
DOI: 10.48550/arxiv.1808.08155

Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
text, January 2006

Hartman, Thomas; Rastelli, Leonardo
arXiv
DOI: 10.48550/arxiv.hep-th/0602106

Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model
text, January 1994

Petkou, Anastasios
arXiv
DOI: 10.48550/arxiv.hep-th/9410093

Correlation functions in the CFT(d)/AdS(d+1) correpondence
text, January 1998

Freedman, Daniel Z.; Mathur, Samir D.; Matusis, Alec
arXiv
DOI: 10.48550/arxiv.hep-th/9804058

AdS/CFT Correspondence and Symmetry Breaking
text, January 1999

Klebanov, Igor R.; Witten, Edward
arXiv
DOI: 10.48550/arxiv.hep-th/9905104

Spinor Exchange in AdS_{d+1}
text, January 1999

Kawano, Teruhiko; Okuyama, Kazumi
arXiv
DOI: 10.48550/arxiv.hep-th/9905130

Works referencing / citing this record:

The analytic functional bootstrap. Part II. Natural bases for the crossing equation
journal, February 2019

Mazáč, Dalimil; Paulos, Miguel F.
Journal of High Energy Physics, Vol. 2019, Issue 2
DOI: 10.1007/jhep02(2019)163

On marginal operators in boundary conformal field theory
journal, October 2019

Herzog, Christopher P.; Shamir, Itamar
Journal of High Energy Physics, Vol. 2019, Issue 10
DOI: 10.1007/jhep10(2019)088

A Mellin Space Approach to Cosmological Correlators
text, January 2019

Sleight, Charlotte
arXiv
DOI: 10.48550/arxiv.1906.12302

Bootstrapping Inflationary Correlators in Mellin Space
text, January 2019

Sleight, Charlotte; Taronna, Massimo
arXiv
DOI: 10.48550/arxiv.1907.01143

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Title: A study of quantum field theories in AdS at finite coupling

Abstract

Citation Formats

Anti-de Sitter space, thermal phase transition, and confinement in gauge theories journal, January 1998

Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models journal, November 1966

Conformal Bootstrap in Mellin Space journal, February 2017

The analytic bootstrap and AdS superhorizon locality journal, December 2013

Spinning AdS loop diagrams: two point functions journal, June 2018

Critical Behavior of a Semi-infinite System: n -Vector Model in the Large- n Limit journal, April 1977

Nambu-Goldstone bosons in curved spacetime journal, November 1985

Adding flavour to the S-matrix bootstrap journal, December 2018

An algebraic approach to the analytic bootstrap journal, April 2017

Curved four dimensional space time as infrared regulator in superstring theories journal, April 1995

The spectrum in the Sachdev-Ye-Kitaev model journal, April 2016

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large n Gauge Theories conference, January 2012

On non-supersymmetric conformal manifolds: field theory and holography journal, November 2017

Analyticity in spin in conformal theories journal, September 2017

Stability in gauged extended supergravity journal, December 1982

Quantum field theory in the large N limit: a review journal, October 2003

The bootstrap program for boundary CFT d journal, July 2013

Loops in Anti–de Sitter Space journal, September 2018

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

On the Polyakov-Mellin bootstrap journal, December 2018

Analyticity and the holographic S-matrix journal, October 2012

Eikonal methods in AdS/CFT: BFKL Pomeron at weak coupling journal, June 2008

A tauberian theorem for the conformal bootstrap journal, December 2017

Spinor exchange in AdSd+1 journal, January 2000

Infrared behavior at negative curvature journal, August 1990

Scale invariance, conformality, and generalized free fields journal, February 2016

Confinement in anti-de Sitter space journal, February 2013

Conformal field theories in anti-de Sitter space journal, February 2011

Analytic bounds and emergence of AdS2 physics from the conformal bootstrap journal, April 2017

Global aspects of current algebra journal, August 1983

The 1/n Expansion for the n-Vector Model in the Semi-Infinite Space journal, November 1983

A spacetime derivation of the Lorentzian OPE inversion formula journal, July 2018

Strings from massive higher spins: the asymptotic uniqueness of the Veneziano amplitude journal, October 2017

Anomalous dimensions in the WF O(N) model with a monodromy line defect journal, March 2018

Universality at large transverse spin in defect CFT journal, September 2018

Bootstrapping 3D fermions journal, March 2016

Crossing symmetry in alpha space journal, November 2017

Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions journal, December 2012

Propagators and effective potentials in anti-de Sitter space journal, March 1985

Large Spin Perturbation Theory for Conformal Field Theories journal, September 2017

Writing CFT correlation functions as AdS scattering amplitudes journal, March 2011

S-matrix bootstrap for resonances journal, September 2018

One loop tests of higher spin AdS/CFT journal, December 2013

A natural language for AdS/CFT correlators journal, November 2011

Dynamical symmetry breaking in four-fermion interaction models journal, June 1991

Universality at large transverse spin in defect CFT text, January 2018

RG stability of integrable fishnet models journal, June 2017

Convexity and liberation at large spin journal, November 2013

Exactly marginal deformations and global symmetries journal, June 2010

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories journal, January 2004

A Mellin space approach to the conformal bootstrap journal, May 2017

Unitarity, crossing symmetry and duality of the S-matrix in large N Chern-Simons theories with fundamental matter journal, April 2015

The S-matrix bootstrap II: two dimensional amplitudes journal, November 2017

Conformal manifolds: ODEs from OPEs journal, March 2018

Supersymmetry in anti-de Sitter space journal, April 1986

Bounding scalar operator dimensions in 4 D CFT journal, December 2008

An investigation of finite size scaling journal, January 1982

Conserved Currents, Consistency Relations, and Operator Product Expansions in the Conformally InvariantO(N) Vector Model journal, July 1996

Effective conformal theory and the flat-space limit of AdS journal, July 2011

One-Loop Effective Potential in Anti-de Sitter Space journal, April 1985

Loops in AdS from conformal field theory journal, July 2017

Ads/CFT correspondence and symmetry breaking journal, September 1999

Unitarity and the holographic S-Matrix journal, October 2012

Four-fermion interaction near four dimensions journal, December 1991

A note on the S-matrix bootstrap for the 2d O(N) bosonic model journal, November 2018

The lightcone bootstrap and the spectrum of the 3d Ising CFT journal, March 2017

Infinite conformal symmetry in two-dimensional quantum field theory journal, July 1984

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

The O( N ) model on a squashed S 3 and the Klebanov-Polyakov correspondence journal, June 2005

Analytic bootstrap for boundary CFT journal, January 2019

Scaling Theory for Finite-Size Effects in the Critical Region journal, June 1972

The S-matrix bootstrap. Part I: QFT in AdS journal, November 2017

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

The renormalization group and the ε expansion journal, August 1974

There are no Goldstone bosons in two dimensions journal, December 1973

Action principle for OPE journal, January 2018

Structure of Phenomenological Lagrangians. I journal, January 1969

Anti-de Sitter space, thermal phase transition, and confinement in gauge theories
journal, January 1998

Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models
journal, November 1966

Conformal Bootstrap in Mellin Space
journal, February 2017

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

Spinning AdS loop diagrams: two point functions
journal, June 2018

Critical Behavior of a Semi-infinite System: $n$ -Vector Model in the Large- $n$ Limit
journal, April 1977

Nambu-Goldstone bosons in curved spacetime
journal, November 1985

Adding flavour to the S-matrix bootstrap
journal, December 2018

An algebraic approach to the analytic bootstrap
journal, April 2017

Curved four dimensional space time as infrared regulator in superstring theories
journal, April 1995

The spectrum in the Sachdev-Ye-Kitaev model
journal, April 2016

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large n Gauge Theories
conference, January 2012

On non-supersymmetric conformal manifolds: field theory and holography
journal, November 2017

Analyticity in spin in conformal theories
journal, September 2017

Stability in gauged extended supergravity
journal, December 1982

Quantum field theory in the large N limit: a review
journal, October 2003

The bootstrap program for boundary CFT d
journal, July 2013

Loops in Anti–de Sitter Space
journal, September 2018

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

On the Polyakov-Mellin bootstrap
journal, December 2018

Analyticity and the holographic S-matrix
journal, October 2012

Eikonal methods in AdS/CFT: BFKL Pomeron at weak coupling
journal, June 2008

A tauberian theorem for the conformal bootstrap
journal, December 2017

Spinor exchange in AdSd+1
journal, January 2000

Infrared behavior at negative curvature
journal, August 1990

Scale invariance, conformality, and generalized free fields
journal, February 2016

Confinement in anti-de Sitter space
journal, February 2013

Conformal field theories in anti-de Sitter space
journal, February 2011

Analytic bounds and emergence of AdS2 physics from the conformal bootstrap
journal, April 2017

Global aspects of current algebra
journal, August 1983

The 1/n Expansion for the n-Vector Model in the Semi-Infinite Space
journal, November 1983

A spacetime derivation of the Lorentzian OPE inversion formula
journal, July 2018

Strings from massive higher spins: the asymptotic uniqueness of the Veneziano amplitude
journal, October 2017

Anomalous dimensions in the WF O(N) model with a monodromy line defect
journal, March 2018

Universality at large transverse spin in defect CFT
journal, September 2018

Bootstrapping 3D fermions
journal, March 2016

Crossing symmetry in alpha space
journal, November 2017

Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions
journal, December 2012

Propagators and effective potentials in anti-de Sitter space
journal, March 1985

Large Spin Perturbation Theory for Conformal Field Theories
journal, September 2017

Writing CFT correlation functions as AdS scattering amplitudes
journal, March 2011

S-matrix bootstrap for resonances
journal, September 2018

One loop tests of higher spin AdS/CFT
journal, December 2013

A natural language for AdS/CFT correlators
journal, November 2011

Dynamical symmetry breaking in four-fermion interaction models
journal, June 1991

Universality at large transverse spin in defect CFT
text, January 2018

RG stability of integrable fishnet models
journal, June 2017

Convexity and liberation at large spin
journal, November 2013

Exactly marginal deformations and global symmetries
journal, June 2010

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories
journal, January 2004

A Mellin space approach to the conformal bootstrap
journal, May 2017

Unitarity, crossing symmetry and duality of the S-matrix in large N Chern-Simons theories with fundamental matter
journal, April 2015

The S-matrix bootstrap II: two dimensional amplitudes
journal, November 2017

Conformal manifolds: ODEs from OPEs
journal, March 2018

Supersymmetry in anti-de Sitter space
journal, April 1986

Bounding scalar operator dimensions in 4 D CFT
journal, December 2008

An investigation of finite size scaling
journal, January 1982

Conserved Currents, Consistency Relations, and Operator Product Expansions in the Conformally InvariantO(N) Vector Model
journal, July 1996

Effective conformal theory and the flat-space limit of AdS
journal, July 2011

One-Loop Effective Potential in Anti-de Sitter Space
journal, April 1985

Loops in AdS from conformal field theory
journal, July 2017

Ads/CFT correspondence and symmetry breaking
journal, September 1999

Unitarity and the holographic S-Matrix
journal, October 2012

Four-fermion interaction near four dimensions
journal, December 1991

A note on the S-matrix bootstrap for the 2d O(N) bosonic model
journal, November 2018

The lightcone bootstrap and the spectrum of the 3d Ising CFT
journal, March 2017

Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984

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

The O( N ) model on a squashed S ³ and the Klebanov-Polyakov correspondence
journal, June 2005

Analytic bootstrap for boundary CFT
journal, January 2019

Scaling Theory for Finite-Size Effects in the Critical Region
journal, June 1972

The S-matrix bootstrap. Part I: QFT in AdS
journal, November 2017

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

The renormalization group and the ε expansion
journal, August 1974

There are no Goldstone bosons in two dimensions
journal, December 1973

Action principle for OPE
journal, January 2018

Structure of Phenomenological Lagrangians. I
journal, January 1969

Structure of Phenomenological Lagrangians. II
journal, January 1969

Renormalization of the Nonlinear $σ$ Model in $2 + ε$ Dimensions—Application to the Heisenberg Ferromagnets
journal, March 1976

Conformal field theories near a boundary in general dimensions
journal, September 1995