Abstract
We consider the tree-level scattering amplitudes in the NS-NS (Neveu-Schwarz) massless sector of closed superstrings in the case where one external state becomes soft. We compute the amplitudes generically for any number of dimensions and any number and kind of the massless closed states through the subsubleading order in the soft expansion. We show that, when the soft state is a graviton or a dilaton, the full result can be expressed as a soft theorem factorizing the amplitude in a soft and a hard part. This behavior is similar to what has previously been observed in field theory and in the bosonic string. Differently from the bosonic string, the supersymmetric soft theorem for the graviton has no string corrections at subsubleading order. The dilaton soft theorem, on the other hand, is found to be universally free of string corrections in any string theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Di Vecchia, R. Marotta and M. Mojaza, Soft theorem for the graviton, dilaton and the Kalb-Ramond field in the bosonic string, JHEP 05 (2015) 137 [arXiv:1502.05258] [INSPIRE].
P. Di Vecchia, R. Marotta and M. Mojaza, Subsubleading soft theorems of gravitons and dilatons in the bosonic string, JHEP 06 (2016) 054 [arXiv:1604.03355] [INSPIRE].
S. Weinberg, Photons and Gravitons in s Matrix Theory: Derivation of Charge Conservation and Equality of Gravitational and Inertial Mass, Phys. Rev. 135 (1964) B1049.
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516.
D.J. Gross and R. Jackiw, Low-Energy Theorem for Graviton Scattering, Phys. Rev. 166 (1968) 1287 [INSPIRE].
R. Jackiw, Low-Energy Theorems for Massless Bosons: Photons and Gravitons, Phys. Rev. 168 (1968) 1623 [INSPIRE].
M. Ademollo et al., Soft Dilatons and Scale Renormalization in Dual Theories, Nucl. Phys. B 94 (1975) 221.
J.A. Shapiro, On the Renormalization of Dual Models, Phys. Rev. D 11 (1975) 2937 [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
J. Broedel, M. de Leeuw, J. Plefka and M. Rosso, Constraining subleading soft gluon and graviton theorems, Phys. Rev. D 90 (2014) 065024 [arXiv:1406.6574] [INSPIRE].
Z. Bern, S. Davies, P. Di Vecchia and J. Nohle, Low-Energy Behavior of Gluons and Gravitons from Gauge Invariance, Phys. Rev. D 90 (2014) 084035 [arXiv:1406.6987] [INSPIRE].
A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].
T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05 (2015) 151 [arXiv:1401.7026] [INSPIRE].
B.U.W. Schwab and A. Volovich, Subleading Soft Theorem in Arbitrary Dimensions from Scattering Equations, Phys. Rev. Lett. 113 (2014) 101601 [arXiv:1404.7749] [INSPIRE].
Z. Bern, S. Davies and J. Nohle, On Loop Corrections to Subleading Soft Behavior of Gluons and Gravitons, Phys. Rev. D 90 (2014) 085015 [arXiv:1405.1015] [INSPIRE].
S. He, Y.-t. Huang and C. Wen, Loop Corrections to Soft Theorems in Gauge Theories and Gravity, JHEP 12 (2014) 115 [arXiv:1405.1410] [INSPIRE].
A.J. Larkoski, Conformal Invariance of the Subleading Soft Theorem in Gauge Theory, Phys. Rev. D 90 (2014) 087701 [arXiv:1405.2346] [INSPIRE].
N. Afkhami-Jeddi, Soft Graviton Theorem in Arbitrary Dimensions, arXiv:1405.3533 [INSPIRE].
C.D. White, Diagrammatic insights into next-to-soft corrections, Phys. Lett. B 737 (2014) 216 [arXiv:1406.7184] [INSPIRE].
M. Zlotnikov, Sub-sub-leading soft-graviton theorem in arbitrary dimension, JHEP 10 (2014) 148 [arXiv:1407.5936] [INSPIRE].
C. Kalousios and F. Rojas, Next to subleading soft-graviton theorem in arbitrary dimensions, JHEP 01 (2015) 107 [arXiv:1407.5982] [INSPIRE].
Y.-J. Du, B. Feng, C.-H. Fu and Y. Wang, Note on Soft Graviton theorem by KLT Relation, JHEP 11 (2014) 090 [arXiv:1408.4179] [INSPIRE].
D. Bonocore, E. Laenen, L. Magnea, L. Vernazza and C.D. White, The method of regions and next-to-soft corrections in Drell-Yan production, Phys. Lett. B 742 (2015) 375 [arXiv:1410.6406] [INSPIRE].
A. Sabio Vera and M.A. Vazquez-Mozo, The Double Copy Structure of Soft Gravitons, JHEP 03 (2015) 070 [arXiv:1412.3699] [INSPIRE].
A.E. Lipstein, Soft Theorems from Conformal Field Theory, JHEP 06 (2015) 166 [arXiv:1504.01364] [INSPIRE].
S.D. Alston, D.C. Dunbar and W.B. Perkins, n-point amplitudes with a single negative-helicity graviton, Phys. Rev. D 92 (2015) 065024 [arXiv:1507.08882] [INSPIRE].
J. Rao and B. Feng, Note on Identities Inspired by New Soft Theorems, JHEP 04 (2016) 173 [arXiv:1604.00650] [INSPIRE].
P. Di Vecchia, R. Marotta, M. Mojaza and J. Nohle, New soft theorems for the gravity dilaton and the Nambu-Goldstone dilaton at subsubleading order, Phys. Rev. D 93 (2016) 085015 [arXiv:1512.03316] [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny and J. Trnka, Effective Field Theories from Soft Limits of Scattering Amplitudes, Phys. Rev. Lett. 114 (2015) 221602 [arXiv:1412.4095] [INSPIRE].
R.H. Boels and W. Wormsbecher, Spontaneously broken conformal invariance in observables, arXiv:1507.08162 [INSPIRE].
Y.-t. Huang and C. Wen, Soft theorems from anomalous symmetries, JHEP 12 (2015) 143 [arXiv:1509.07840] [INSPIRE].
I. Low, Double Soft Theorems and Shift Symmetry in Nonlinear σ-models, Phys. Rev. D 93 (2016) 045032 [arXiv:1512.01232] [INSPIRE].
H. Lüo and C. Wen, Recursion relations from soft theorems, JHEP 03 (2016) 088 [arXiv:1512.06801] [INSPIRE].
M. Bianchi, A.L. Guerrieri, Y.-t. Huang, C.-J. Lee and C. Wen, Exploring soft constraints on effective actions, JHEP 10 (2016) 036 [arXiv:1605.08697] [INSPIRE].
B.U.W. Schwab, Subleading Soft Factor for String Disk Amplitudes, JHEP 08 (2014) 062 [arXiv:1406.4172] [INSPIRE].
M. Bianchi, S. He, Y.-t. Huang and C. Wen, More on Soft Theorems: Trees, Loops and Strings, Phys. Rev. D 92 (2015) 065022 [arXiv:1406.5155] [INSPIRE].
B.U.W. Schwab, A Note on Soft Factors for Closed String Scattering, JHEP 03 (2015) 140 [arXiv:1411.6661] [INSPIRE].
M. Bianchi and A.L. Guerrieri, On the soft limit of open string disk amplitudes with massive states, JHEP 09 (2015) 164 [arXiv:1505.05854] [INSPIRE].
A.L. Guerrieri, Soft behavior of string amplitudes with external massive states, Nuovo Cim. C 39 (2016) 221 [arXiv:1507.08829] [INSPIRE].
P. Di Vecchia, R. Marotta and M. Mojaza, Soft Theorems from String Theory, Fortsch. Phys. 64 (2016) 389 [arXiv:1511.04921] [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: 1610.03481
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
Di Vecchia, P., Marotta, R. & Mojaza, M. Soft behavior of a closed massless state in superstring and universality in the soft behavior of the dilaton. J. High Energ. Phys. 2016, 20 (2016). https://doi.org/10.1007/JHEP12(2016)020
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2016)020