Abstract
We consider weakly coupled theories of massive higher-spin particles. This class of models includes, for instance, tree-level String Theory and Large-N Yang-Mills theory. The S-matrix in such theories is a meromorphic function obeying unitarity and crossing symmetry. We discuss the (unphysical) regime s, t ≫ 1, in which we expect the amplitude to be universal and exponentially large. We develop methods to study this regime and show that the amplitude necessarily coincides with the Veneziano amplitude there. In particular, this implies that the leading Regge trajectory, j(t), is asymptotically linear in Yang-Mills theory. Further, our analysis shows that any such theory of higherspin particles has stringy excitations and infinitely many asymptotically parallel subleading trajectories. More generally, we argue that, under some assumptions, any theory with at least one higher-spin particle must have strings.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Veneziano, Construction of a crossing-symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cim. A 57 (1968) 190 [INSPIRE].
G. ’t Hooft, A Planar Diagram Theory for Strong Interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
E. Witten, Baryons in the 1/n Expansion, Nucl. Phys. B 160 (1979) 57 [INSPIRE].
X.O. Camanho, J.D. Edelstein, J. Maldacena and A. Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling, JHEP 02 (2016) 020 [arXiv:1407.5597] [INSPIRE].
S.B. Giddings and R.A. Porto, The Gravitational S-matrix, Phys. Rev. D 81 (2010) 025002 [arXiv:0908.0004] [INSPIRE].
R. Dolen, D. Horn and C. Schmid, Finite energy sum rules and their application to pi N charge exchange, Phys. Rev. 166 (1968) 1768 [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. Polchinski and M.J. Strassler, The string dual of a confining four-dimensional gauge theory, hep-th/0003136.
D.J. Gross and P.F. Mende, The High-Energy Behavior of String Scattering Amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].
M. Karliner, I.R. Klebanov and L. Susskind, Size and Shape of Strings, Int. J. Mod. Phys. A 3 (1988) 1981 [INSPIRE].
L. Susskind, Strings, black holes and Lorentz contraction, Phys. Rev. D 49 (1994) 6606 [hep-th/9308139] [INSPIRE].
R.C. Brower, J. Polchinski, M.J. Strassler and C.-I. Tan, The Pomeron and gauge/string duality, JHEP 12 (2007) 005 [hep-th/0603115] [INSPIRE].
Y. Makeenko and P. Olesen, Wilson Loops and QCD/String Scattering Amplitudes, Phys. Rev. D 80 (2009) 026002 [arXiv:0903.4114] [INSPIRE].
A. Armoni, Large-N QCD and the Veneziano Amplitude, Phys. Lett. B 756 (2016) 328 [arXiv:1509.03077] [INSPIRE].
I.R. Klebanov and A.M. Polyakov, AdS dual of the critical O(N ) vector model, Phys. Lett. B 550 (2002) 213 [hep-th/0210114] [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories: Star product and AdS space, in The many faces of the superworld, M.A. Shifman ed., pg. 533-610, World Scientific (2000) [hep-th/9910096].
D.D. Coon, Uniqueness of the veneziano representation, Phys. Lett. B 29 (1969) 669 [INSPIRE].
S. Matsuda, Uniqueness of the veneziano representation, Phys. Rev. 185 (1969) 1811 [INSPIRE].
N.N. Khuri, Derivation of a veneziano series from the Regge representation, Phys. Rev. 185 (1969) 1876 [INSPIRE].
R.H. Boels and T. Hansen, String theory in target space, JHEP 06 (2014) 054 [arXiv:1402.6356] [INSPIRE].
S. Mandelstam, Dual-Resonance Models, Phys. Rept. 13 (1974) 259 [INSPIRE].
S. Dubovsky, R. Flauger and V. Gorbenko, Effective String Theory Revisited, JHEP 09 (2012) 044 [arXiv:1203.1054] [INSPIRE].
J. Polchinski and A. Strominger, Effective string theory, Phys. Rev. Lett. 67 (1991) 1681 [INSPIRE].
O. Aharony and Z. Komargodski, The Effective Theory of Long Strings, JHEP 05 (2013) 118 [arXiv:1302.6257] [INSPIRE].
S. Hellerman, S. Maeda, J. Maltz and I. Swanson, Effective String Theory Simplified, JHEP 09 (2014) 183 [arXiv:1405.6197] [INSPIRE].
S. Hellerman and I. Swanson, String Theory of the Regge Intercept, Phys. Rev. Lett. 114 (2015) 111601 [arXiv:1312.0999] [INSPIRE].
L.A. Pando Zayas, J. Sonnenschein and D. Vaman, Regge trajectories revisited in the gauge/string correspondence, Nucl. Phys. B 682 (2004) 3 [hep-th/0311190] [INSPIRE].
A. Karch, E. Katz, D.T. Son and M.A. Stephanov, Linear confinement and AdS/QCD, Phys. Rev. D 74 (2006) 015005 [hep-ph/0602229] [INSPIRE].
H.B. Meyer and M.J. Teper, Glueball Regge trajectories and the Pomeron: A Lattice study, Phys. Lett. B 605 (2005) 344 [hep-ph/0409183] [INSPIRE].
G. Wanders, Constraints on the zeros and the asymptotic behavior of a veneziano amplitude, Phys. Lett. B 34 (1971) 325 [INSPIRE].
D. Sivers and J. Yellin, Review of recent work on narrow resonance models, Rev. Mod. Phys. 43 (1971) 125 [INSPIRE].
I.E. Pritsker and A.M. Yeager, Zeros of Polynomials with Random Coefficients, J. Approx. Theory 189 (2015) 88 [arXiv:1407.6769].
W.V. Assche, Some results on the asymptotic distribution of the zeros of orthogonal polynomials, Comput. Math. Appl. 12-13 (1985) 615.
T. Tao and V. Vu, Local universality of zeroes of random polynomials, arXiv:1307.4357.
D.J. Gross and J.L. Manes, The High-energy Behavior of Open String Scattering, Nucl. Phys. B 326 (1989) 73 [INSPIRE].
S. Rychkov, EPFL Lectures on Conformal Field Theory in D¿= 3 Dimensions, arXiv:1601.05000.
M. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, 2d S-matrix Bootstrap, to appear.
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].
Z. Komargodski and A. Zhiboedov, Convexity and Liberation at Large Spin, JHEP 11 (2013) 140 [arXiv:1212.4103] [INSPIRE].
S. El-Showk, M.F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, Solving the 3D Ising Model with the Conformal Bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping Mixed Correlators in the 3D Ising Model, JHEP 11 (2014) 109 [arXiv:1406.4858] [INSPIRE].
N. Arkani-Hamed, Y.T. Huang and T.C. Huang, String theory as the unique weakly-coupled UV Completion of YM and GR, in progress.
J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025 [arXiv:1011.1485] [INSPIRE].
N. Arkani-Hamed and J. Maldacena, Cosmological Collider Physics, arXiv:1503.08043 [INSPIRE].
A. Strominger, Quantum Gravity and String Theory, talk at Strings 2014, Princeton, U.S.A. (2014).
J. Maldacena and A. Zhiboedov, Constraining conformal field theories with a slightly broken higher spin symmetry, Class. Quant. Grav. 30 (2013) 104003 [arXiv:1204.3882] [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Superstring Collisions at Planckian Energies, Phys. Lett. B 197 (1987) 81 [INSPIRE].
G.P. Korchemsky, J. Kotanski and A.N. Manashov, Multi-reggeon compound states and resummed anomalous dimensions in QCD, Phys. Lett. B 583 (2004) 121 [hep-ph/0306250] [INSPIRE].
P.G.O. Freund, finite energy sum rules and bootstraps, Phys. Rev. Lett. 20 (1968) 235 [INSPIRE].
Z. Komargodski and A. Schwimmer, unpublished (2013).
M. Bochicchio, Glueball and meson propagators of any spin in large-N QCD, Nucl. Phys. B 875 (2013) 621 [arXiv:1305.0273] [INSPIRE].
M. Bochicchio and S.P. Muscinelli, Ultraviolet asymptotics of glueball propagators, JHEP 08 (2013) 064 [arXiv:1304.6409] [INSPIRE].
D. Pappadopulo, S. Rychkov, J. Espin and R. Rattazzi, OPE Convergence in Conformal Field Theory, Phys. Rev. D 86 (2012) 105043 [arXiv:1208.6449] [INSPIRE].
D.B. Fairlie and J. Nuyts, A fresh look at generalized Veneziano amplitudes, Nucl. Phys. B 433 (1995) 26 [hep-th/9406043] [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: 1607.04253
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
Caron-Huot, S., Komargodski, Z., Sever, A. et al. Strings from massive higher spins: the asymptotic uniqueness of the Veneziano amplitude. J. High Energ. Phys. 2017, 26 (2017). https://doi.org/10.1007/JHEP10(2017)026
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)026