Abstract
We report on non-perturbative bounds for structure constants on \( \mathcal{N}=4 \) SYM. Such bounds are obtained by applying the conformal bootstrap recently extended to super-conformal theories. We compare our results with interpolating functions suitably restricted by the S-duality of the theory. Within numerical errors, these interpolations support the conjecture that the bounds found in this paper are saturated at duality invariant values of the coupling. This extends recent conjectures for the anomalous dimension of leading twist operators.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].
V.S. Rychkov and A. Vichi, Universal constraints on conformal operator dimensions, Phys. Rev. D 80 (2009) 045006 [arXiv:0905.2211] [INSPIRE].
S. El-Showk et al., Solving the 3D Ising model with the conformal bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].
F. Caracciolo and V.S. Rychkov, Rigorous limits on the interaction strength in quantum field theory, Phys. Rev. D 81 (2010) 085037 [arXiv:0912.2726] [INSPIRE].
D. Poland and D. Simmons-Duffin, Bounds on 4D conformal and superconformal field theories, JHEP 05 (2011) 017 [arXiv:1009.2087] [INSPIRE].
S. El-Showk and M.F. Paulos, Bootstrapping conformal field theories with the extremal functional method, Phys. Rev. Lett. 111 (2013) 241601 [arXiv:1211.2810] [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, The \( \mathcal{N}=4 \) superconformal bootstrap, Phys. Rev. Lett. 111 (2013) 071601 [arXiv:1304.1803] [INSPIRE].
B. Eden, A.C. Petkou, C. Schubert and E. Sokatchev, Partial nonrenormalization of the stress tensor four point function in \( \mathcal{N}=4 \) SYM and AdS/CFT, Nucl. Phys. B 607 (2001) 191 [hep-th/0009106] [INSPIRE].
F.A. Dolan and H. Osborn, Superconformal symmetry, correlation functions and the operator product expansion, Nucl. Phys. B 629 (2002) 3 [hep-th/0112251] [INSPIRE].
B. Eden and E. Sokatchev, On the OPE of 1/2 BPS short operators in \( \mathcal{N}=4 \) SCFT 4, Nucl. Phys. B 618 (2001) 259 [hep-th/0106249] [INSPIRE].
C. Beem, L. Rastelli, A. Sen and B.C. van Rees, Resummation and S-duality in \( \mathcal{N}=4 \) SYM, JHEP 04 (2014) 122 [arXiv:1306.3228] [INSPIRE].
B. Eden, Three-loop universal structure constants in \( \mathcal{N}=4 \) SUSY Yang-Mills theory, arXiv:1207.3112 [INSPIRE].
A. Sen, S-duality improved superstring perturbation theory, JHEP 11 (2013) 029 [arXiv:1304.0458] [INSPIRE].
L.F. Alday and A. Bissi, Higher-spin correlators, JHEP 10 (2013) 202 [arXiv:1305.4604] [INSPIRE].
Z. Komargodski and A. Zhiboedov, Convexity and liberation at large spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].
A.L. Fitzpatrick, J. Kaplan, D. Poland and D. Simmons-Duffin, The analytic bootstrap and AdS superhorizon locality, JHEP 12 (2013) 004 [arXiv:1212.3616] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1310.3757
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Alday, L.F., Bissi, A. The superconformal bootstrap for structure constants. J. High Energ. Phys. 2014, 144 (2014). https://doi.org/10.1007/JHEP09(2014)144
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2014)144