Abstract
The set of double-logarithmic (DL) contributions (α t ln2s)n to the 4-graviton amplitude in \( \mathcal{N} \) = 8 supergravity (SUGRA), with α being the gravitational coupling and (s, t) the Mandelstam invariants, is studied in impact parameter (ρ) representation. This sector of the amplitude shows interesting properties which shed light on the nature of quantum corrections in gravity. Besides having a convergent behaviour as s increases, which is not present in \( \mathcal{N} \)< 4 SUGRA theories, there exists a critical line ρc(s) above which the Born amplitude prevails. The short distance region ρ < ρc(s) is dominated by the DL terms. As a consequence, when studied in terms of an eikonal approach in the forward limit, the scattering angle linked to the bending of the semiclassical trajectory of the graviton shows a transition from attractive gravity at large distances to a region at small ρ characterized by a repulsive DL contribution to the gravitational potential due to the gravitino content of the theory. In the complex angular momentum plane, this DL high energy asymptotics is driven by the rightmost pole singularity of a parabolic cylinder function. The resummation of DL quantum corrections in \( \mathcal{N} \) = 8 SUGRA can be understood in terms of the counting of 1-rooted maps on orientable surfaces.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
Z. Bern, J.J.M. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The Complete Four-Loop Four-Point Amplitude in N = 4 Super-Yang-Mills Theory, Phys. Rev.D 82 (2010) 125040 [arXiv:1008.3327] [INSPIRE].
Z. Bern, Perturbative quantum gravity and its relation to gauge theory, Living Rev. Rel.5 (2002) 5 [gr-qc/0206071] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar, M. Perelstein and J.S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys.B 530 (1998) 401 [hep-th/9802162] [INSPIRE].
Z. Bern, J.J. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, The Ultraviolet Behavior of N = 8 Supergravity at Four Loops, Phys. Rev. Lett.103(2009) 081301 [arXiv:0905.2326] [INSPIRE].
M.T. Grisaru, P. van Nieuwenhuizen and C.C. Wu, Reggeization and the Question of Higher Loop Renormalizability of Gravitation, Phys. Rev.D 12 (1975) 1563 [INSPIRE].
M.T. Grisaru and H.J. Schnitzer, Dynamical Calculation of Bound State Supermultiplets in N = 8 Supergravity,Phys. Lett.B 107(1981) 196 [INSPIRE].
L.N. Lipatov, Graviton Reggeization, Phys. Lett.B 116 (1982) 411 [INSPIRE].
L.N. Lipatov, Multi-Regge Processes in Gravitation, Sov. Phys. JETP55 (1982) 582 [Zh. Eksp. Teor. Fiz.82 (1982) 991] [INSPIRE].
L.N. Lipatov, High-energy scattering in QCD and in quantum gravity and two-dimensional field theories, Nucl. Phys.B 365 (1991) 614 [INSPIRE].
L.N. Lipatov, Effective action for the Regge processes in gravity, Phys. Part. Nucl.44 (2013) 391 [arXiv:1105.3127] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev.D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
L.N. Lipatov, Reggeization of the Vector Meson and the Vacuum Singularity in Nonabelian Gauge Theories, Sov. J. Nucl. Phys.23 (1976) 338 [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, On the Pomeranchuk Singularity in Asymptotically Free Theories, Phys. Lett.B 60 (1975) 50 [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, Multi-Reggeon Processes in the Yang-Mills Theory, Sov. Phys. JETP44 (1976) 443 [Zh. Eksp. Teor. Fiz.71 (1976) 840] [INSPIRE].
E.A. Kuraev, L.N. Lipatov and V.S. Fadin, The Pomeranchuk Singularity in Nonabelian Gauge Theories, Sov. Phys. JETP45 (1977) 199 [Zh. Eksp. Teor. Fiz.72 (1977) 377] [INSPIRE].
I.I. Balitsky and L.N. Lipatov, The Pomeranchuk Singularity in Quantum Chromodynamics, Sov. J. Nucl. Phys.28 (1978) 822 [INSPIRE].
A. Sabio Vera, E. Serna Campillo and M. Á. Vázquez-Mozo, Graviton emission in Einstein-Hilbert gravity, JHEP03 (2012) 005 [arXiv:1112.4494] [INSPIRE].
A. Sabio Vera, E. Serna Campillo and M. Á. Vázquez-Mozo, Color-Kinematics Duality and the Regge Limit of Inelastic Amplitudes, JHEP04 (2013) 086 [arXiv:1212.5103] [INSPIRE].
H. Johansson, A. Sabio Vera, E. Serna Campillo and M. Á. Vázquez-Mozo, Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction, JHEP10 (2013) 215 [arXiv:1307.3106] [INSPIRE].
A. Sabio Vera and M. Á. Vázquez-Mozo, The Double Copy Structure of Soft Gravitons, JHEP03 (2015) 070 [arXiv:1412.3699] [INSPIRE].
J. Bartels, L.N. Lipatov and A. Sabio Vera, Double-logarithms in Einstein-Hilbert gravity and supergravity, JHEP07 (2014) 056 [arXiv:1208.3423] [INSPIRE].
C. Boucher-Veronneau and L.J. Dixon, \( \mathcal{N} \) ≥ 4 Supergravity Amplitudes from Gauge Theory at Two Loops, JHEP12 (2011) 046 [arXiv:1110.1132] [INSPIRE].
J.M. Henn and B. Mistlberger, Four-graviton scattering to three loops in \( \mathcal{N} \) = 8 supergravity, JHEP05 (2019) 023 [arXiv:1902.07221] [INSPIRE].
R.J. Martin and M.J. Kearney, An exactly solvable self-convolutive recurrence, Aequationes Math.80 (2010) 291 [arXiv:1103.4936] [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev.140 (1965) B516 [INSPIRE].
R. Kirschner and L.N. Lipatov, Double Logarithmic Asymptotics of Quark Scattering Amplitudes With Flavor Exchange, Phys. Rev.D 26 (1982) 1202 [INSPIRE].
R. Kirschner and L.N. Lipatov, Doubly Logarithmic Asymptotic Of The Quark Scattering Amplitude With Nonvacuum Exchange In The T Channel, Sov. Phys. JETP56 (1982) 266 [Zh. Eksp. Teor. Fiz.83 (1982) 488] [INSPIRE].
R. Kirschner and L.N. Lipatov, Double Logarithmic Asymptotics and Regge Singularities of Quark Amplitudes with Flavor Exchange, Nucl. Phys.B 213 (1983) 122 [INSPIRE].
E. Ihrig, G. Rosensteel, H. Chow and L.E.H. Trainor, Group theory and many body diagrams II. Enumeration methods and number approximations, Proc. Roy. Soc. Lond.A 348 (1976) 339.
P. Cvitanovic, B.E. Lautrup and R.B. Pearson, The Number and Weights of Feynman Diagrams, Phys. Rev.D 18 (1978) 1939 [INSPIRE].
G.L. Goodvin, M. Berciu and G.A. Sawatzky, The Green’s function of the Holstein polaron, Phys. Rev.B 74 (2006) 245104.
A.K. Collado, P. Di Vecchia, R. Russo and S. Thomas, The subleading eikonal in supergravity theories, JHEP10 (2018) 038 [arXiv:1807.04588] [INSPIRE].
H.-H. Chi, Graviton Bending in Quantum Gravity from One-Loop Amplitudes, Phys. Rev.D 99 (2019) 126008 [arXiv:1903.07944] [INSPIRE].
D. Arquès and J-F. Béraud, Rooted maps on orientable surfaces, Riccati’s equation and continued fractions, Discrete Math.215 (2000) 1 [hal-00693781].
A. Prunotto, W.M. Alberico and P. Czerski, Feynman Diagrams and Rooted Maps, Open Phys.16 (2018) 149 [arXiv:1312.0934] [INSPIRE].
K.K. Gopala, P. Labelle and V. Shramchenko, Enumeration of N -rooted maps using quantum field theory, Nucl. Phys.B 936 (2018) 668 [arXiv:1709.01200] [INSPIRE].
K. Gopala Krishna, P. Labelle and V. Shramchenko, Feynman diagrams, ribbon graphs and topological recursion of Eynard-Orantin, JHEP06 (2018) 162 [arXiv:1802.01773] [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: 1904.13372
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Vera, A.S. Double-logarithms in \( \mathcal{N} \) = 8 supergravity: impact parameter description & mapping to 1-rooted ribbon graphs. J. High Energ. Phys. 2019, 80 (2019). https://doi.org/10.1007/JHEP07(2019)080
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2019)080