Abstract
We calculate the simultaneous double-soft limit of two massless closed strings scattering with any number of closed string tachyons to the subleading order at the tree level. The limit factorizes the scattering amplitude into a double-soft factor multiplying the pure tachyon subamplitude, suggesting a universal double-soft theorem for the massless closed string. We confirm an existing result for the double-soft graviton in an on-shell equivalent, but different form, while also establishing the double-soft factorization behavior of the string dilaton and of the Kalb-Ramond state, as well as the mixed graviton-dilaton case. We also show that the simultaneous and consecutive double-soft theorems are consistent with each other. We furthermore provide a complete field theory diagrammatic view on our result, which enables us in particular to establish a four-point interaction vertex for two tachyons and two massless closed string states, as well as the missing in field theory of three-point interaction of two massless closed string state and one tachyon.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.A. Shapiro, On the Renormalization of Dual Models, Phys. Rev. D 11 (1975) 2937 [INSPIRE].
M. Ademollo et al., Soft Dilations and Scale Renormalization in Dual Theories, Nucl. Phys. B 94 (1975) 221 [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].
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].
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].
M. Bianchi and A.L. Guerrieri, On the soft limit of closed string amplitudes with massive states, Nucl. Phys. B 905 (2016) 188 [arXiv:1512.00803] [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].
P. Di Vecchia, R. Marotta and M. Mojaza, Soft behavior of a closed massless state in superstring and universality in the soft behavior of the dilaton, JHEP 12 (2016) 020 [arXiv:1610.03481] [INSPIRE].
A. Sen, Soft Theorems in Superstring Theory, JHEP 06 (2017) 113 [arXiv:1702.03934] [INSPIRE].
P. Di Vecchia, R. Marotta and M. Mojaza, The B-field soft theorem and its unification with the graviton and dilaton, JHEP 10 (2017) 017 [arXiv:1706.02961] [INSPIRE].
S. Higuchi and H. Kawai, Universality of soft theorem from locality of soft vertex operators, Nucl. Phys. B 936 (2018) 400 [arXiv:1805.11079] [INSPIRE].
R. Marotta and M. Verma, Soft Theorems from Compactification, JHEP 02 (2020) 008 [arXiv:1911.05099] [INSPIRE].
A. Sen, Subleading Soft Graviton Theorem for Loop Amplitudes, JHEP 11 (2017) 123 [arXiv:1703.00024] [INSPIRE].
P. Vecchia, R. Marotta and M. Mojaza, Multiloop Soft Theorem for Gravitons and Dilatons in the Bosonic String, JHEP 01 (2019) 038 [arXiv:1808.04845] [INSPIRE].
P. Di Vecchia, R. Marotta and M. Mojaza, Multiloop soft theorem of the dilaton in the bosonic string, Phys. Rev. D 100 (2019) 041902 [arXiv:1907.01036] [INSPIRE].
P. Di Vecchia, R. Marotta and M. Mojaza, Double-soft behavior for scalars and gluons from string theory, JHEP 12 (2015) 150 [arXiv:1507.00938] [INSPIRE].
T. Klose, T. McLoughlin, D. Nandan, J. Plefka and G. Travaglini, Double-Soft Limits of Gluons and Gravitons, arXiv:1504.05558 [INSPIRE].
N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the Simplest Quantum Field Theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].
Y. Wang and X. Yin, Constraining Higher Derivative Supergravity with Scattering Amplitudes, Phys. Rev. D 92 (2015) 041701 [arXiv:1502.03810] [INSPIRE].
M.B. Green and C. Wen, Modular Forms and SL(2, ℤ)-covariance of type IIB superstring theory, JHEP 06 (2019) 087 [arXiv:1904.13394] [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].
P. Di Vecchia, R. Marotta and M. Mojaza, Double-soft behavior of the dilaton of spontaneously broken conformal invariance, JHEP 09 (2017) 001 [arXiv:1705.06175] [INSPIRE].
A.L. Guerrieri, Y.-t. Huang, Z. Li and C. Wen, On the exactness of soft theorems, JHEP 12 (2017) 052 [arXiv:1705.10078] [INSPIRE].
S. Chakrabarti, S.P. Kashyap, B. Sahoo, A. Sen and M. Verma, Subleading Soft Theorem for Multiple Soft Gravitons, JHEP 12 (2017) 150 [arXiv:1707.06803] [INSPIRE].
S. Chakrabarti, S.P. Kashyap, B. Sahoo, A. Sen and M. Verma, Testing Subleading Multiple Soft Graviton Theorem for CHY Prescription, JHEP 01 (2018) 090 [arXiv:1709.07883] [INSPIRE].
J. Scherk, Zero-slope limit of the dual resonance model, Nucl. Phys. B 31 (1971) 222 [INSPIRE].
E. Witten, The Feynman i in String Theory, JHEP 04 (2015) 055 [arXiv:1307.5124] [INSPIRE].
A.A. Tseytlin, σ-model approach to string theory effective actions with tachyons, J. Math.Phys. 42 (2001) 2854 [hep-th/0011033] [INSPIRE].
A. Koemans Collado, P. Di Vecchia and R. Russo, Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes, Phys. Rev. D 100 (2019) 066028 [arXiv:1904.02667] [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: 2005.05877
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
Marotta, R., Mojaza, M. Double-soft behavior of massless closed strings interacting with any number of closed string tachyons. J. High Energ. Phys. 2020, 83 (2020). https://doi.org/10.1007/JHEP08(2020)083
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2020)083