More analytic bootstrap: nonperturbative effects and fermions

Albayrak, Soner; Meltzer, David; Poland, David

doi:10.1007/jhep08(2019)040

Title: More analytic bootstrap: nonperturbative effects and fermions

Abstract

We develop the analytic bootstrap in several directions. First, we discuss the appearance of nonperturbative effects in the Lorentzian inversion formula, which are exponentially suppressed at large spin but important at finite spin. We show that these effects are important for precision applications of the analytic bootstrap in the context of the 3d Ising and O(2) models. In the former they allow us to reproduce the spin-2 stress tensor with error at the 10^-5 level while in the latter requiring that we reproduce the stress tensor allows us to predict the coupling to the leading charge-2 operator. We also extend perturbative calculations in the lightcone bootstrap to fermion 4-point functions in 3d, predicting the leading and subleading asymptotic behavior for the double-twist operators built out of two fermions.

Authors:

Albayrak, Soner ^[1]; Meltzer, David ^[1]; Poland, David ^[1]

Yale Univ., New Haven, CT (United States); California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

Publication Date:: 2019-08-07

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation; National Science Foundation (NSF); Sherman Fairchild Foundation

OSTI Identifier:: 1611636

Grant/Contract Number:: SC0011632; 488651; PHY-1350180

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: 8; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Conformal and W Symmetry; Conformal Field Theory; Nonperturbative Effects

Citation Formats


                    Albayrak, Soner, Meltzer, David, and Poland, David. More analytic bootstrap: nonperturbative effects and fermions.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep08(2019)040.

Copy to clipboard


                    Albayrak, Soner, Meltzer, David, & Poland, David. More analytic bootstrap: nonperturbative effects and fermions.  United States.  https://doi.org/10.1007/jhep08(2019)040

Copy to clipboard


                    Albayrak, Soner, Meltzer, David, and Poland, David. Wed .  
"More analytic bootstrap: nonperturbative effects and fermions".  United States.  https://doi.org/10.1007/jhep08(2019)040.  https://www.osti.gov/servlets/purl/1611636.

Copy to clipboard


                    
@article{osti_1611636,

  title        = {More analytic bootstrap: nonperturbative effects and fermions},

  author       = {Albayrak, Soner and Meltzer, David and Poland, David},

  abstractNote = {We develop the analytic bootstrap in several directions. First, we discuss the appearance of nonperturbative effects in the Lorentzian inversion formula, which are exponentially suppressed at large spin but important at finite spin. We show that these effects are important for precision applications of the analytic bootstrap in the context of the 3d Ising and O(2) models. In the former they allow us to reproduce the spin-2 stress tensor with error at the 10-5 level while in the latter requiring that we reproduce the stress tensor allows us to predict the coupling to the leading charge-2 operator. We also extend perturbative calculations in the lightcone bootstrap to fermion 4-point functions in 3d, predicting the leading and subleading asymptotic behavior for the double-twist operators built out of two fermions.},

  doi          = {10.1007/jhep08(2019)040},

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

  number       = 8,

  volume       = 2019,

  place        = {United States},

  year         = {2019},

  month        = {8}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1007/jhep08(2019)040

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 30 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Einstein gravity 3-point functions from conformal field theory
journal, December 2017

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan
Journal of High Energy Physics, Vol. 2017, Issue 12
DOI: 10.1007/JHEP12(2017)049

Bootstrapping 3D fermions
journal, March 2016

Iliesiu, Luca; Kos, Filip; Poland, David
Journal of High Energy Physics, Vol. 2016, Issue 3
DOI: 10.1007/JHEP03(2016)120

The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019

Poland, David; Rychkov, Slava; Vichi, Alessandro
Reviews of Modern Physics, Vol. 91, Issue 1
DOI: 10.1103/RevModPhys.91.015002

Comments on operators with large spin
journal, November 2007

Alday, Luis F.; Maldacena, Juan
Journal of High Energy Physics, Vol. 2007, Issue 11
DOI: 10.1088/1126-6708/2007/11/019

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

Alday, Luis F.
Physical Review Letters, Vol. 119, Issue 11
DOI: 10.1103/PhysRevLett.119.111601

Bootstrapping the O(N) archipelago
journal, November 2015

Kos, Filip; Poland, David; Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2015, Issue 11
DOI: 10.1007/JHEP11(2015)106

Weight shifting operators and conformal blocks
journal, February 2018

Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2018, Issue 2
DOI: 10.1007/JHEP02(2018)081

Bootstrapping the O(N ) vector models
journal, June 2014

Kos, Filip; Poland, David; Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2014, Issue 6
DOI: 10.1007/JHEP06(2014)091

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David
Journal of High Energy Physics, Vol. 2013, Issue 12
DOI: 10.1007/JHEP12(2013)004

Anomalous dimensions at finite conformal spin from OPE inversion
journal, November 2018

Cardona, Carlos; Sen, Kallol
Journal of High Energy Physics, Vol. 2018, Issue 11
DOI: 10.1007/JHEP11(2018)052

Precision islands in the Ising and O(N ) models
journal, August 2016

Kos, Filip; Poland, David; Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2016, Issue 8
DOI: 10.1007/JHEP08(2016)036

Conformal collider physics from the lightcone bootstrap
journal, February 2016

Li, Daliang; Meltzer, David; Poland, David
Journal of High Energy Physics, Vol. 2016, Issue 2
DOI: 10.1007/JHEP02(2016)143

Conformal Regge theory
journal, December 2012

Costa, Miguel S.; Goncalves, Vasco; Penedones, João
Journal of High Energy Physics, Vol. 2012, Issue 12
DOI: 10.1007/JHEP12(2012)091

Mellin space bootstrap for global symmetry
journal, July 2017

Dey, Parijat; Kaviraj, Apratim; Sinha, Aninda
Journal of High Energy Physics, Vol. 2017, Issue 7
DOI: 10.1007/JHEP07(2017)019

An algebraic approach to the analytic bootstrap
journal, April 2017

Alday, Luis F.; Zhiboedov, Alexander
Journal of High Energy Physics, Vol. 2017, Issue 4
DOI: 10.1007/JHEP04(2017)157

Bounds for OPE coefficients on the Regge trajectory
journal, October 2017

Costa, Miguel S.; Hansen, Tobias; Penedones, João
Journal of High Energy Physics, Vol. 2017, Issue 10
DOI: 10.1007/JHEP10(2017)197

Convexity and liberation at large spin
journal, November 2013

Komargodski, Zohar; Zhiboedov, Alexander
Journal of High Energy Physics, Vol. 2013, Issue 11
DOI: 10.1007/JHEP11(2013)140

Fermion conformal bootstrap in 4d
journal, June 2019

Karateev, Denis; Kravchuk, Petr; Serone, Marco
Journal of High Energy Physics, Vol. 2019, Issue 6
DOI: 10.1007/JHEP06(2019)088

Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
journal, July 2018

Sleight, Charlotte; Taronna, Massimo
Fortschritte der Physik, Vol. 66, Issue 8-9
DOI: 10.1002/prop.201800038

Spinning conformal correlators
journal, November 2011

Costa, Miguel S.; Penedones, João; Poland, David
Journal of High Energy Physics, Vol. 2011, Issue 11
DOI: 10.1007/JHEP11(2011)071

Analyticity in spin in conformal theories
journal, September 2017

Caron-Huot, Simon
Journal of High Energy Physics, Vol. 2017, Issue 9
DOI: 10.1007/JHEP09(2017)078

Beyond a = c : gravitational couplings to matter and the stress tensor OPE
journal, July 2018

Meltzer, David; Perlmutter, Eric
Journal of High Energy Physics, Vol. 2018, Issue 7
DOI: 10.1007/JHEP07(2018)157

Bootstrapping 3D fermions with global symmetries
journal, January 2018

Iliesiu, Luca; Kos, Filip; Poland, David
Journal of High Energy Physics, Vol. 2018, Issue 1
DOI: 10.1007/JHEP01(2018)036

Conformal bootstrap in the Regge limit
journal, December 2017

Li, Daliang; Meltzer, David; Poland, David
Journal of High Energy Physics, Vol. 2017, Issue 12
DOI: 10.1007/JHEP12(2017)013

A conformal collider for holographic CFTs
journal, October 2018

Afkhami-Jeddi, Nima; Kundu, Sandipan; Tajdini, Amirhossein
Journal of High Energy Physics, Vol. 2018, Issue 10
DOI: 10.1007/JHEP10(2018)156

A proof of the conformal collider bounds
journal, June 2016

Hofman, Diego M.; Li, Daliang; Meltzer, David
Journal of High Energy Physics, Vol. 2016, Issue 6
DOI: 10.1007/JHEP06(2016)111

Scalar-fermion analytic bootstrap in 4D
journal, June 2019

Elkhidir, Emtinan; Karateev, Denis
Journal of High Energy Physics, Vol. 2019, Issue 6
DOI: 10.1007/JHEP06(2019)026

Bulk phase shift, CFT Regge limit and Einstein gravity
journal, June 2018

Kulaxizi, Manuela; Parnachev, Andrei; Zhiboedov, Alexander
Journal of High Energy Physics, Vol. 2018, Issue 6
DOI: 10.1007/JHEP06(2018)121

Anomalous dimensions from crossing kernels
journal, November 2018

Sleight, Charlotte; Taronna, Massimo
Journal of High Energy Physics, Vol. 2018, Issue 11
DOI: 10.1007/JHEP11(2018)089

Dimensional reduction for conformal blocks
journal, September 2016

Hogervorst, Matthijs
Journal of High Energy Physics, Vol. 2016, Issue 9
DOI: 10.1007/JHEP09(2016)017

Light-ray operators in conformal field theory
journal, November 2018

Kravchuk, Petr; Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2018, Issue 11
DOI: 10.1007/JHEP11(2018)102

Shockwaves from the operator product expansion
journal, March 2019

Afkhami-Jeddi, Nima; Hartman, Thomas; Kundu, Sandipan
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/JHEP03(2019)201

Bootstrapping the minimal 3D SCFT
journal, November 2018

Atanasov, Alexander; Hillman, Aaron; Poland, David
Journal of High Energy Physics, Vol. 2018, Issue 11
DOI: 10.1007/JHEP11(2018)140

Resummation at finite conformal spin
journal, January 2019

Cardona, Carlos; Guha, Sunny; Kanumilli, Surya Kiran
Journal of High Energy Physics, Vol. 2019, Issue 1
DOI: 10.1007/JHEP01(2019)077

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

Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2017, Issue 3
DOI: 10.1007/JHEP03(2017)086

Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973

Ferrara, S.; Grillo, A. F.; Gatto, R.
Annals of Physics, Vol. 76, Issue 1
DOI: 10.1016/0003-4916(73)90446-6

d-dimensional SYK, AdS loops, and 6j symbols
journal, March 2019

Liu, Junyu; Perlmutter, Eric; Rosenhaus, Vladimir
Journal of High Energy Physics, Vol. 2019, Issue 3
DOI: 10.1007/JHEP03(2019)052

Bootstrapping mixed correlators in the 3D Ising model
journal, November 2014

Kos, Filip; Poland, David; Simmons-Duffin, David
Journal of High Energy Physics, Vol. 2014, Issue 11
DOI: 10.1007/JHEP11(2014)109

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

Simmons-Duffin, David; Stanford, Douglas; Witten, Edward
Journal of High Energy Physics, Vol. 2018, Issue 7
DOI: 10.1007/JHEP07(2018)085

Similar Records in DOE PAGES and OSTI.GOV collections:

The 3d stress-tensor bootstrap

Journal Article Dymarsky, Anatoly ; Kos, Filip ; Kravchuk, Petr ; ... - Journal of High Energy Physics (Online)

We study the conformal bootstrap for 4-point functions of stress tensors in parity-preserving 3d CFTs. To set up the bootstrap equations, we analyze the constraints of conformal symmetry, permutation symmetry, and conservation on the stress-tensor 4-point function and identify a non-redundant set of crossing equations. Studying these equations numerically using semidefinite optimization, we compute bounds on the central charge as a function of the independent coefficient in the stress-tensor 3-point function. With no additional assumptions, these bounds numerically reproduce the conformal collider bounds and give a general lower bound on the central charge. We also study the effect of gapsmore »« less
Cited by 51
https://doi.org/10.1007/JHEP02(2018)164

Full Text Available
Bootstrapping 3D fermions with global symmetries

Journal Article Iliesiu, Luca ; Kos, Filip ; Poland, David ; ... - Journal of High Energy Physics (Online)

We study the conformal bootstrap for 4-point functions of fermions < ψ _i ψ _j ψ _k ψ _ℓ > in parity-preserving 3d CFTs, where ψ _i transforms as a vector under an O(N ) global symmetry. We compute bounds on scaling dimensions and central charges, finding features in our bounds that appear to coincide with the O(N ) symmetric Gross-Neveu-Yukawa fixed points. Our computations are in perfect agreement with the 1/N expansion at large N and allow us to make nontrivial predictions at small N . For values of N for which the Gross-Neveu-Yukawa universality classes are relevant tomore »« less
Cited by 51
https://doi.org/10.1007/jhep01(2018)036

Full Text Available
The lightcone bootstrap and the spectrum of the 3d Ising CFT

Journal Article Simmons-Duffin, David - Journal of High Energy Physics (Online)

In this paper. we compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques for computing infinite sums of SL(2,R) conformal blocks. Using these techniques, we solve the lightcone bootstrap to all orders in an asymptotic expansion in large spin, and suggest a strategy for going beyond the large spin limit. We carry out the first steps of this strategy for the 3d Ising CFT, deriving analytic approximations for the dimensions and OPE coefficients of several infinite families of operators in terms of the initial datamore »« less
Cited by 158
https://doi.org/10.1007/JHEP03(2017)086

Full Text Available
Bootstrapping mixed correlators in three-dimensional cubic theories II

Journal Article Kousvos, Stefanos R. ; Stergiou, Andreas - SciPost Physics Proceedings

Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the \varepsilon ε expansion. In an earlier work, we used the nonperturbative numerical conformal bootstrap to provide evidence for the existence of a previously unknown 3D CFT with cubic symmetry, dubbed “Platonic CFT”. In this work, we make further use of the numerical conformal bootstrap to perform a three-dimensional scan in the space of scaling dimensions of three low-lying operators. We find a three-dimensional isolated allowedmore »« less
Cited by 11
https://doi.org/10.21468/SciPostPhys.8.6.085
Bootstrapping the 3d Ising model at finite temperature

Journal Article Iliesiu, Luca ; Koloğlu, Murat ; Simmons-Duffin, David - Journal of High Energy Physics (Online)

We estimate thermal one-point functions in the 3d Ising CFT using the operator product expansion (OPE) and the Kubo-Martin-Schwinger (KMS) condition. Several operator dimensions and OPE coefficients of the theory are known from the numerical bootstrap for flat-space four-point functions. Taking this data as input, we use a thermal Lorentzian inversion formula to compute thermal one-point coefficients of the first few Regge trajectories in terms of a small number of unknown parameters. We approximately determine the unknown parameters by imposing the KMS condition on the two-point functions (σσ) and (ϵϵ). As a result, we estimate the one-point functions of the lowest-dimensionmore »« less
https://doi.org/10.1007/JHEP12(2019)072

Full Text Available

Similar Records

Title: More analytic bootstrap: nonperturbative effects and fermions

Abstract

Citation Formats

Einstein gravity 3-point functions from conformal field theory journal, December 2017

Bootstrapping 3D fermions journal, March 2016

The conformal bootstrap: Theory, numerical techniques, and applications journal, January 2019

Comments on operators with large spin journal, November 2007

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

Bootstrapping the O(N) archipelago journal, November 2015

Weight shifting operators and conformal blocks journal, February 2018

Bootstrapping the O(N ) vector models journal, June 2014

The analytic bootstrap and AdS superhorizon locality journal, December 2013

Anomalous dimensions at finite conformal spin from OPE inversion journal, November 2018

Precision islands in the Ising and O(N ) models journal, August 2016

Conformal collider physics from the lightcone bootstrap journal, February 2016

Conformal Regge theory journal, December 2012

Mellin space bootstrap for global symmetry journal, July 2017

An algebraic approach to the analytic bootstrap journal, April 2017

Bounds for OPE coefficients on the Regge trajectory journal, October 2017

Convexity and liberation at large spin journal, November 2013

Fermion conformal bootstrap in 4d journal, June 2019

Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications journal, July 2018

Spinning conformal correlators journal, November 2011

Analyticity in spin in conformal theories journal, September 2017

Beyond a = c : gravitational couplings to matter and the stress tensor OPE journal, July 2018

Bootstrapping 3D fermions with global symmetries journal, January 2018

Conformal bootstrap in the Regge limit journal, December 2017

A conformal collider for holographic CFTs journal, October 2018

A proof of the conformal collider bounds journal, June 2016

Scalar-fermion analytic bootstrap in 4D journal, June 2019

Bulk phase shift, CFT Regge limit and Einstein gravity journal, June 2018

Anomalous dimensions from crossing kernels journal, November 2018

Dimensional reduction for conformal blocks journal, September 2016

Light-ray operators in conformal field theory journal, November 2018

Shockwaves from the operator product expansion journal, March 2019

Bootstrapping the minimal 3D SCFT journal, November 2018

Resummation at finite conformal spin journal, January 2019

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

Tensor representations of conformal algebra and conformally covariant operator product expansion journal, March 1973

d-dimensional SYK, AdS loops, and 6j symbols journal, March 2019

Bootstrapping mixed correlators in the 3D Ising model journal, November 2014

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

Einstein gravity 3-point functions from conformal field theory
journal, December 2017

Bootstrapping 3D fermions
journal, March 2016

The conformal bootstrap: Theory, numerical techniques, and applications
journal, January 2019

Comments on operators with large spin
journal, November 2007

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

Bootstrapping the O(N) archipelago
journal, November 2015

Weight shifting operators and conformal blocks
journal, February 2018

Bootstrapping the O(N ) vector models
journal, June 2014

The analytic bootstrap and AdS superhorizon locality
journal, December 2013

Anomalous dimensions at finite conformal spin from OPE inversion
journal, November 2018

Precision islands in the Ising and O(N ) models
journal, August 2016

Conformal collider physics from the lightcone bootstrap
journal, February 2016

Conformal Regge theory
journal, December 2012

Mellin space bootstrap for global symmetry
journal, July 2017

An algebraic approach to the analytic bootstrap
journal, April 2017

Bounds for OPE coefficients on the Regge trajectory
journal, October 2017

Convexity and liberation at large spin
journal, November 2013

Fermion conformal bootstrap in 4d
journal, June 2019

Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
journal, July 2018

Spinning conformal correlators
journal, November 2011

Analyticity in spin in conformal theories
journal, September 2017

Beyond a = c : gravitational couplings to matter and the stress tensor OPE
journal, July 2018

Bootstrapping 3D fermions with global symmetries
journal, January 2018

Conformal bootstrap in the Regge limit
journal, December 2017

A conformal collider for holographic CFTs
journal, October 2018

A proof of the conformal collider bounds
journal, June 2016

Scalar-fermion analytic bootstrap in 4D
journal, June 2019

Bulk phase shift, CFT Regge limit and Einstein gravity
journal, June 2018

Anomalous dimensions from crossing kernels
journal, November 2018

Dimensional reduction for conformal blocks
journal, September 2016

Light-ray operators in conformal field theory
journal, November 2018

Shockwaves from the operator product expansion
journal, March 2019

Bootstrapping the minimal 3D SCFT
journal, November 2018

Resummation at finite conformal spin
journal, January 2019

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

Tensor representations of conformal algebra and conformally covariant operator product expansion
journal, March 1973

d-dimensional SYK, AdS loops, and 6j symbols
journal, March 2019

Bootstrapping mixed correlators in the 3D Ising model
journal, November 2014

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