Abstract
We count the number of independent solutions to crossing constraints of four point functions involving charged scalars and charged fermions in a CFT with large gap in the spectrum. To find the CFT data we employ recently developed analytical functionals to charged fields. We compute the corresponding higher dimensional flat space S matrices in an independent group theoretic manner and obtain agreement with our CFT counting of ambiguities. We also write down the local lagrangians explicitly. Our work lends further evidence to [1] that any CFT with a large central charge expansion and a large gap in the spectrum has an AdS bulk dual.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
I. Heemskerk, J. Penedones, J. Polchinski and J. Sully, Holography from conformal field theory, JHEP 10 (2009) 079 [arXiv:0907.0151] [INSPIRE].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
I. Heemskerk and J. Sully, More holography from conformal field theory, JHEP 09 (2010) 099 [arXiv:1006.0976] [INSPIRE].
S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, AdS bulk locality from sharp CFT bounds, arXiv:2106.10274 [INSPIRE].
S. Kundu, Swampland conditions for higher derivative couplings from CFT, arXiv:2104.11238 [INSPIRE].
D. Mazáč, L. Rastelli and X. Zhou, A basis of analytic functionals for CFTs in general dimension, JHEP 08 (2021) 140 [arXiv:1910.12855] [INSPIRE].
S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, Dispersive CFT sum rules, JHEP 05 (2021) 243 [arXiv:2008.04931] [INSPIRE].
S. El-Showk and M.F. Paulos, Extremal bootstrapping: go with the flow, JHEP 03 (2018) 148 [arXiv:1605.08087] [INSPIRE].
D. Mazac and M.F. Paulos, The analytic functional bootstrap. Part I. 1D CFTs and 2D S-matrices, JHEP 02 (2019) 162 [arXiv:1803.10233] [INSPIRE].
D. Mazac and M.F. Paulos, The analytic functional bootstrap. Part II. Natural bases for the crossing equation, JHEP 02 (2019) 163 [arXiv:1811.10646] [INSPIRE].
M.F. Paulos, Analytic functional bootstrap for CFTs in d > 1, JHEP 04 (2020) 093 [arXiv:1910.08563] [INSPIRE].
M.F. Paulos and B. Zan, A functional approach to the numerical conformal bootstrap, JHEP 09 (2020) 006 [arXiv:1904.03193] [INSPIRE].
M.F. Paulos, Dispersion relations and exact bounds on CFT correlators, JHEP 08 (2021) 166 [arXiv:2012.10454] [INSPIRE].
K. Ghosh, A. Kaviraj and M.F. Paulos, Charging up the functional bootstrap, arXiv:2107.00041 [INSPIRE].
S.D. Chowdhury, A. Gadde, T. Gopalka, I. Halder, L. Janagal and S. Minwalla, Classifying and constraining local four photon and four graviton S-matrices, JHEP 02 (2020) 114 [arXiv:1910.14392] [INSPIRE].
S.D. Chowdhury and A. Gadde, Classification of four-point local gluon S-matrices, JHEP 01 (2021) 104 [arXiv:2006.12458] [INSPIRE].
D. Li, D. Meltzer and D. Poland, Non-Abelian binding energies from the lightcone bootstrap, JHEP 02 (2016) 149 [arXiv:1510.07044] [INSPIRE].
R. Rattazzi, S. Rychkov and A. Vichi, Bounds in 4D conformal field theories with global symmetry, J. Phys. A 44 (2011) 035402 [arXiv:1009.5985] [INSPIRE].
A. Vichi, Improved bounds for CFT’s with global symmetries, JHEP 01 (2012) 162 [arXiv:1106.4037] [INSPIRE].
D. Poland, D. Simmons-Duffin and A. Vichi, Carving out the space of 4D CFTs, JHEP 05 (2012) 110 [arXiv:1109.5176] [INSPIRE].
F. Kos, D. Poland, D. Simmons-Duffin and A. Vichi, Bootstrapping the O(N ) archipelago, JHEP 11 (2015) 106 [arXiv:1504.07997] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping the O(N ) vector models, JHEP 06 (2014) 091 [arXiv:1307.6856] [INSPIRE].
M. Hogervorst and S. Rychkov, Radial coordinates for conformal blocks, Phys. Rev. D 87 (2013) 106004 [arXiv:1303.1111] [INSPIRE].
P. Cvitanovic, Group theory: Birdtracks, Lie’s and exceptional groups, Princeton University Press, Princeton U.S.A. (2008).
M. Berkooz, R. Yacoby and A. Zait, Bounds on \( \mathcal{N} \) = 1 superconformal theories with global symmetries, JHEP 08 (2014) 008 [Erratum ibid. 01 (2015) 132] [arXiv:1402.6068] [INSPIRE].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn-deconfinement phase transition in weakly coupled large N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [INSPIRE].
B. Sundborg, The Hagedorn transition, deconfinement and N = 4 SYM theory, Nucl. Phys. B 573 (2000) 349 [hep-th/9908001] [INSPIRE].
B. Henning, X. Lu, T. Melia and H. Murayama, Hilbert series and operator bases with derivatives in effective field theories, Commun. Math. Phys. 347 (2016) 363 [arXiv:1507.07240] [INSPIRE].
B. Henning, X. Lu, T. Melia and H. Murayama, Operator bases, S-matrices, and their partition functions, JHEP 10 (2017) 199 [arXiv:1706.08520] [INSPIRE].
R. de Mello Koch, P. Rabambi, R. Rabe and S. Ramgoolam, Counting and construction of holomorphic primary fields in free CFT4 from rings of functions on Calabi-Yau orbifolds, JHEP 08 (2017) 077 [arXiv:1705.06702] [INSPIRE].
R. de Mello Koch and S. Ramgoolam, Free field primaries in general dimensions: counting and construction with rings and modules, JHEP 08 (2018) 088 [arXiv:1806.01085] [INSPIRE].
A. Kobach and S. Pal, Reparameterization Invariant Operator Basis for NRQED and HQET, JHEP 11 (2019) 012 [arXiv:1810.02356] [INSPIRE].
A. Kobach and S. Pal, Hilbert series and operator basis for NRQED and NRQCD/HQET, Phys. Lett. B 772 (2017) 225 [arXiv:1704.00008] [INSPIRE].
T. Melia and S. Pal, EFT asymptotics: the growth of operator degeneracy, SciPost Phys. 10 (2021) 104 [arXiv:2010.08560] [INSPIRE].
M.A.A. van Leeuwen, A.M. Cohen and B. Lisser, LiE, a package for Lie group computations, Computer Algebra Nederland, Amsterdam, The Netherlands.
D. Mazac, Analytic bounds and emergence of AdS2 physics from the conformal bootstrap, JHEP 04 (2017) 146 [arXiv:1611.10060] [INSPIRE].
D. Mazáč, A crossing-symmetric OPE inversion formula, JHEP 06 (2019) 082 [arXiv:1812.02254] [INSPIRE].
A. Kaviraj and M.F. Paulos, The functional bootstrap for boundary CFT, JHEP 04 (2020) 135 [arXiv:1812.04034] [INSPIRE].
D. Mazáč, L. Rastelli and X. Zhou, An analytic approach to BCFTd , JHEP 12 (2019) 004 [arXiv:1812.09314] [INSPIRE].
J. Penedones, J.A. Silva and A. Zhiboedov, Nonperturbative Mellin amplitudes: existence, properties, applications, JHEP 08 (2020) 031 [arXiv:1912.11100] [INSPIRE].
D. Carmi, J. Penedones, J.A. Silva and A. Zhiboedov, Applications of dispersive sum rules: E-expansion and holography, SciPost Phys. 10 (2021) 145 [arXiv:2009.13506] [INSPIRE].
D. Freedman and A. Van Proeyen, Supergravity, Cambridge University Press, Cambridge U.K. (2012).
F.A. Dolan, Character formulae and partition functions in higher dimensional conformal field theory, J. Math. Phys. 47 (2006) 062303 [hep-th/0508031] [INSPIRE].
L.F. Alday, A. Bissi and T. Lukowski, Lessons from crossing symmetry at large N , JHEP 06 (2015) 074 [arXiv:1410.4717] [INSPIRE].
A.L. Fitzpatrick and J. Kaplan, Analyticity and the holographic S-matrix, JHEP 10 (2012) 127 [arXiv:1111.6972] [INSPIRE].
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
L. Iliesiu, F. Kos, D. Poland, S.S. Pufu, D. Simmons-Duffin and R. Yacoby, Bootstrapping 3D fermions, JHEP 03 (2016) 120 [arXiv:1508.00012] [INSPIRE].
S.D. Chowdhury and K. Ghosh, to appear.
A. Hebbar, D. Karateev and J. Penedones, Spinning S-matrix bootstrap in 4d, arXiv:2011.11708 [INSPIRE].
D. Poland and V. Prilepina, Recursion relations for 5-point conformal blocks, arXiv:2103.12092 [INSPIRE].
L. Iliesiu, M. Koloğlu, R. Mahajan, E. Perlmutter and D. Simmons-Duffin, The conformal bootstrap at finite temperature, JHEP 10 (2018) 070 [arXiv:1802.10266] [INSPIRE].
L.F. Alday, M. Kologlu and A. Zhiboedov, Holographic correlators at finite temperature, JHEP 06 (2021) 082 [arXiv:2009.10062] [INSPIRE].
C. Armstrong, A.E. Lipstein and J. Mei, Color/kinematics duality in AdS4 , JHEP 02 (2021) 194 [arXiv:2012.02059] [INSPIRE].
S. Albayrak, S. Kharel and D. Meltzer, On duality of color and kinematics in (A)dS momentum space, JHEP 03 (2021) 249 [arXiv:2012.10460] [INSPIRE].
L.F. Alday, C. Behan, P. Ferrero and X. Zhou, Gluon scattering in AdS from CFT, JHEP 06 (2021) 020 [arXiv:2103.15830] [INSPIRE].
X. Zhou, Double copy relation in AdS space, Phys. Rev. Lett. 127 (2021) 141601 [arXiv:2106.07651] [INSPIRE].
J. Broedel and L.J. Dixon, Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators, JHEP 10 (2012) 091 [arXiv:1208.0876] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal partial waves and the operator product expansion, Nucl. Phys. B 678 (2004) 491 [hep-th/0309180] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal partial waves: further mathematical results, arXiv:1108.6194 [INSPIRE].
S. Jain, M. Mandlik, S. Minwalla, T. Takimi, S.R. Wadia and S. Yokoyama, Unitarity, crossing symmetry and duality of the S-matrix in large N Chern-Simons theories with fundamental matter, JHEP 04 (2015) 129 [arXiv:1404.6373] [INSPIRE].
J. Gray, A. Hanany, Y.-H. He, V. Jejjala and N. Mekareeya, SQCD: a geometric apercu, JHEP 05 (2008) 099 [arXiv:0803.4257] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2107.06266
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Chowdhury, S.D., Ghosh, K. Bulk locality for scalars and fermions with global symmetry. J. High Energ. Phys. 2021, 146 (2021). https://doi.org/10.1007/JHEP10(2021)146
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2021)146