The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT

Liu, Junyu; Meltzer, David; Poland, David; Simmons-Duffin, David

doi:10.1007/jhep09(2020)115

Title: The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT

Journal Article · Thu Sep 17 00:00:00 EDT 2020 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep09(2020)115· OSTI ID:1712432

Liu, Junyu ^[1]; Meltzer, David ^[2]; Poland, David ^[3]; Simmons-Duffin, David ^[2]

California Institute of Technology (CalTech), Pasadena, CA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States). Inst. for Quantum Information and Matter
California Institute of Technology (CalTech), Pasadena, CA (United States)
Yale Univ., New Haven, CT (United States)

We study the spectrum and OPE coefficients of the three-dimensional critical O(2) model, using four-point functions of the leading scalars with charges 0, 1, and 2 (s, $$\phi$$, and t). We obtain numerical predictions for low-twist OPE data in several charge sectors using the extremal functional method. We compare the results to analytical estimates using the Lorentzian inversion formula and a small amount of numerical input. We find agreement between the analytic and numerical predictions. We also give evidence that certain scalar operators lie on double-twist Regge trajectories and obtain estimates for the leading Regge intercepts of the O(2) model.

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States); Yale Univ., New Haven, CT (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation

Grant/Contract Number:: SC0019085; SC0020318; 488657; 488651

OSTI ID:: 1712432

Journal Information:: Journal of High Energy Physics (Online), Vol. 2020, Issue 9; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (61)

RG flow from ϕ 4 theory to the 2D Ising model Anand, Nikhil; Genest, Vincent X.; Katz, Emanuel Journal of High Energy Physics, Vol. 2017, Issue 8 https://doi.org/10.1007/JHEP08(2017)056	journal	August 2017
Eikonalization of conformal blocks Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T. Journal of High Energy Physics, Vol. 2015, Issue 9 https://doi.org/10.1007/JHEP09(2015)019	journal	September 2015
A conformal dispersion relation: correlations from absorption Carmi, Dean; Caron-Huot, Simon Journal of High Energy Physics, Vol. 2020, Issue 9 https://doi.org/10.1007/JHEP09(2020)009	journal	September 2020
The analytic bootstrap and AdS superhorizon locality Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David Journal of High Energy Physics, Vol. 2013, Issue 12 https://doi.org/10.1007/JHEP12(2013)004	journal	December 2013
Conformal Regge theory Costa, Miguel S.; Goncalves, Vasco; Penedones, João Journal of High Energy Physics, Vol. 2012, Issue 12 https://doi.org/10.1007/JHEP12(2012)091	journal	December 2012
Dynamical Response near Quantum Critical Points Lucas, Andrew; Gazit, Snir; Podolsky, Daniel Physical Review Letters, Vol. 118, Issue 5 https://doi.org/10.1103/PhysRevLett.118.056601	journal	February 2017
Taming the ϵ-expansion with large spin perturbation theory Alday, Luis F.; Henriksson, Johan; van Loon, Mark Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/JHEP07(2018)131	journal	July 2018
Analyticity in spin in conformal theories Caron-Huot, Simon Journal of High Energy Physics, Vol. 2017, Issue 9 https://doi.org/10.1007/JHEP09(2017)078	journal	September 2017
Conformal field theories at nonzero temperature: Operator product expansions, Monte Carlo, and holography Katz, Emanuel; Sachdev, Subir; Sørensen, Erik S. Physical Review B, Vol. 90, Issue 24 https://doi.org/10.1103/PhysRevB.90.245109	journal	December 2014
Light-ray operators in conformal field theory Kravchuk, Petr; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2018, Issue 11 https://doi.org/10.1007/JHEP11(2018)102	journal	November 2018
Eikonal approximation in AdS/CFT: Conformal partial waves and finite N four-point functions Cornalba, Lorenzo; Costa, Miguel S.; Penedones, João Nuclear Physics B, Vol. 767, Issue 3 https://doi.org/10.1016/j.nuclphysb.2007.01.007	journal	April 2007
Monte Carlo Renormalization Flows in the Space of Relevant and Irrelevant Operators: Application to Three-Dimensional Clock Models Shao, Hui; Guo, Wenan; Sandvik, Anders W. Physical Review Letters, Vol. 124, Issue 8 https://doi.org/10.1103/PhysRevLett.124.080602	journal	February 2020
Bootstrapping the minimal 3D SCFT Atanasov, Alexander; Hillman, Aaron; Poland, David Journal of High Energy Physics, Vol. 2018, Issue 11 https://doi.org/10.1007/JHEP11(2018)140	journal	November 2018
Monte Carlo study of an improved clock model in three dimensions Hasenbusch, Martin Physical Review B, Vol. 100, Issue 22 https://doi.org/10.1103/PhysRevB.100.224517	journal	December 2019
Resummation at finite conformal spin Cardona, Carlos; Guha, Sunny; Kanumilli, Surya Kiran Journal of High Energy Physics, Vol. 2019, Issue 1 https://doi.org/10.1007/JHEP01(2019)077	journal	January 2019
Closed-form expression for cross-channel conformal blocks near the lightcone Li, Wenliang Journal of High Energy Physics, Vol. 2020, Issue 1 https://doi.org/10.1007/JHEP01(2020)055	journal	January 2020
Higher spin ANEC and the space of CFTs Meltzer, David Journal of High Energy Physics, Vol. 2019, Issue 7 https://doi.org/10.1007/JHEP07(2019)001	journal	July 2019
Conformal collider physics: energy and charge correlations Hofman, Diego M.; Maldacena, Juan Journal of High Energy Physics, Vol. 2008, Issue 05 https://doi.org/10.1088/1126-6708/2008/05/012	journal	May 2008
Non-gaussianity of the critical 3d Ising model Rychkov, Slava; Simmons-Duffin, David; Zan, Bernardo SciPost Physics, Vol. 2, Issue 1 https://doi.org/10.21468/SciPostPhys.2.1.001	journal	January 2017
A semidefinite program solver for the conformal bootstrap Simmons-Duffin, David Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/JHEP06(2015)174	journal	June 2015
The random-bond Ising model in 2.01 and 3 dimensions Komargodski, Zohar; Simmons-Duffin, David Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 15 https://doi.org/10.1088/1751-8121/aa6087	journal	March 2017
Truncated conformal space approach in $d$ dimensions: A cheap alternative to lattice field theory? Hogervorst, Matthijs; Rychkov, Slava; van Rees, Balt C. Physical Review D, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevD.91.025005	journal	January 2015
d-dimensional SYK, AdS loops, and 6j symbols Liu, Junyu; Perlmutter, Eric; Rosenhaus, Vladimir Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/JHEP03(2019)052	journal	March 2019
A spacetime derivation of the Lorentzian OPE inversion formula Simmons-Duffin, David; Stanford, Douglas; Witten, Edward Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/JHEP07(2018)085	journal	July 2018
Bootstrapping the 3d Ising model at finite temperature Iliesiu, Luca; Koloğlu, Murat; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/JHEP12(2019)072	journal	December 2019
Bootstrapping 3D fermions Iliesiu, Luca; Kos, Filip; Poland, David Journal of High Energy Physics, Vol. 2016, Issue 3 https://doi.org/10.1007/JHEP03(2016)120	journal	March 2016
The conformal bootstrap: Theory, numerical techniques, and applications Poland, David; Rychkov, Slava; Vichi, Alessandro Reviews of Modern Physics, Vol. 91, Issue 1 https://doi.org/10.1103/RevModPhys.91.015002	journal	January 2019
AdS/CFT unitarity at higher loops: high-energy string scattering Meltzer, David Journal of High Energy Physics, Vol. 2020, Issue 5 https://doi.org/10.1007/JHEP05(2020)133	journal	May 2020
Large Spin Perturbation Theory for Conformal Field Theories Alday, Luis F. Physical Review Letters, Vol. 119, Issue 11 https://doi.org/10.1103/PhysRevLett.119.111601	journal	September 2017
Constraining Quantum Critical Dynamics: $(2 + 1) D$ Ising Model and Beyond Witczak-Krempa, William Physical Review Letters, Vol. 114, Issue 17 https://doi.org/10.1103/PhysRevLett.114.177201	journal	April 2015
Bootstrapping the O(N) archipelago Kos, Filip; Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2015, Issue 11 https://doi.org/10.1007/JHEP11(2015)106	journal	November 2015
Carving out OPE space and precise O(2) model critical exponents Chester, Shai M.; Landry, Walter; Liu, Junyu Journal of High Energy Physics, Vol. 2020, Issue 6 https://doi.org/10.1007/JHEP06(2020)142	journal	June 2020
Precision islands in the Ising and O(N ) models Kos, Filip; Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)036	journal	August 2016
Lightcone effective Hamiltonians and RG flows Fitzpatrick, A. Liam; Kaplan, Jared; Katz, Emanuel Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/JHEP08(2018)120	journal	August 2018
Exploring Hamiltonian truncation in $d = 2 + 1$ Elias-Miró, Joan; Hardy, Edward Physical Review D, Vol. 102, Issue 6 https://doi.org/10.1103/PhysRevD.102.065001	journal	September 2020
Bounds on 4D conformal and superconformal field theories Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)017	journal	May 2011
Convexity and liberation at large spin Komargodski, Zohar; Zhiboedov, Alexander Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)140	journal	November 2013
Hamiltonian truncation study of the $ϕ^{4}$ theory in two dimensions. II. The $Z_{2}$ -broken phase and the Chang duality Rychkov, Slava; Vitale, Lorenzo G. Physical Review D, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevD.93.065014	journal	March 2016
High-precision calculations in strongly coupled quantum field theory with next-to-leading-order renormalized Hamiltonian Truncation Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G. Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/JHEP10(2017)213	journal	October 2017
The conformal bootstrap at finite temperature Iliesiu, Luca; Koloğlu, Murat; Mahajan, Raghu Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/JHEP10(2018)070	journal	October 2018
Conformal truncation of chern-simons theory at large Nf Delacrétaz, Luca V.; Fitzpatrick, A. Liam; Katz, Emanuel Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/JHEP03(2019)107	journal	March 2019
Conformal bootstrap in the Regge limit Li, Daliang; Meltzer, David; Poland, David Journal of High Energy Physics, Vol. 2017, Issue 12 https://doi.org/10.1007/JHEP12(2017)013	journal	December 2017
Eikonal approximation in AdS/CFT: resumming the gravitational loop expansion Cornalba, Lorenzo; Costa, Miguel S.; Penedones, João Journal of High Energy Physics, Vol. 2007, Issue 09 https://doi.org/10.1088/1126-6708/2007/09/037	journal	September 2007
Implications of Conformal Invariance in Field Theories for General Dimensions Osborn, H.; Petkou, A. Annals of Physics, Vol. 231, Issue 2 https://doi.org/10.1006/aphy.1994.1045	journal	May 1994
Dimensional reduction for conformal blocks Hogervorst, Matthijs Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)017	journal	September 2016
NLO renormalization in the Hamiltonian truncation Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G. Physical Review D, Vol. 96, Issue 6 https://doi.org/10.1103/PhysRevD.96.065024	journal	September 2017
The lightcone bootstrap and the spectrum of the 3d Ising CFT Simmons-Duffin, David Journal of High Energy Physics, Vol. 2017, Issue 3 https://doi.org/10.1007/JHEP03(2017)086	journal	March 2017
Analytic functional bootstrap for CFTs in d > 1 Paulos, Miguel F. Journal of High Energy Physics, Vol. 2020, Issue 4 https://doi.org/10.1007/JHEP04(2020)093	journal	April 2020
Diagonal limit for conformal blocks in d dimensions Hogervorst, Matthijs; Osborn, Hugh; Rychkov, Slava Journal of High Energy Physics, Vol. 2013, Issue 8 https://doi.org/10.1007/JHEP08(2013)014	journal	August 2013
The conformal bootstrap Poland, David; Simmons-Duffin, David Nature Physics, Vol. 12, Issue 6 https://doi.org/10.1038/nphys3761	journal	June 2016
Bootstrapping the (A1, A2) Argyres-Douglas theory Cornagliotto, Martina; Lemos, Madalena; Liendo, Pedro Journal of High Energy Physics, Vol. 2018, Issue 3 https://doi.org/10.1007/JHEP03(2018)033	journal	March 2018
Bootstrapping 3D fermions with global symmetries Iliesiu, Luca; Kos, Filip; Poland, David Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/jhep01(2018)036	journal	January 2018
autoboot: a generator of bootstrap equations with global symmetry Go, Mocho; Tachikawa, Yuji Journal of High Energy Physics, Vol. 2019, Issue 6 https://doi.org/10.1007/jhep06(2019)084	journal	June 2019
A conformal truncation framework for infinite-volume dynamics Katz, Emanuel; Khandker, Zuhair U.; Walters, Matthew T. Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/jhep07(2016)140	journal	July 2016
Quantum critical response: from conformal perturbation theory to holography Lucas, Andrew; Sierens, Todd; Witczak-Krempa, William Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/jhep07(2017)149	journal	July 2017
Towards bootstrapping QED3 Chester, Shai M.; Pufu, Silviu S. Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/jhep08(2016)019	journal	August 2016
Anisotropic perturbations in three-dimensional O( $N$ )-symmetric vector models Hasenbusch, Martin; Vicari, Ettore Physical Review B, Vol. 84, Issue 12 https://doi.org/10.1103/physrevb.84.125136	journal	September 2011
Bootstrapping Conformal Field Theories with the Extremal Functional Method El-Showk, Sheer; Paulos, Miguel F. Physical Review Letters, Vol. 111, Issue 24 https://doi.org/10.1103/physrevlett.111.241601	journal	December 2013
Diagonal Limit for Conformal Blocks in d Dimensions Hogervorst, Matthijs; Osborn, Hugh; Rychkov, Slava arXiv https://doi.org/10.48550/arxiv.1305.1321	text	January 2013
Dimensional Reduction for Conformal Blocks Hogervorst, Matthijs arXiv https://doi.org/10.48550/arxiv.1604.08913	text	January 2016
Variations of Seasonal Precipitation in the Yellow River Basin and Its Relationship to General Circulation and SST Liu, Jing; Jin, Lijun; Huang, Changxing Proceedings of the International Association of Hydrological Sciences, Vol. 383 https://doi.org/10.5194/piahs-383-5-2020	journal	September 2020

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