Abstract
We use insights from superstring field theory to prove the subleading soft graviton theorem for tree amplitudes of (compactified) heterotic and type II string theories for arbitrary number of finite energy NS (NSNS) sector external states but only one soft graviton. We also prove the leading soft graviton theorem in these theories for arbitrary number of external soft gravitons. In our analysis there is no restriction on the mass and spin of the finite energy external states. This method can also be used to give a proof of the subleading soft graviton theorem for tree amplitudes in quantum field theories coupled to gravity with generic interactions. We discuss the technical issue involved in extending this analysis to loop amplitudes of superstring theory including Ramond sector external states, and its possible resolution.
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References
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 [INSPIRE].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [INSPIRE].
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].
C.D. White, Factorization properties of soft graviton amplitudes, JHEP 05 (2011) 060 [arXiv:1103.2981] [INSPIRE].
F. Cachazo and A. Strominger, Evidence for a new soft graviton theorem, arXiv:1404.4091 [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].
F. Cachazo and E.Y. Yuan, Are soft theorems renormalized?, arXiv:1405.3413 [INSPIRE].
N. Afkhami-Jeddi, Soft graviton theorem in arbitrary dimensions, arXiv:1405.3533 [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].
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].
F. Cachazo, S. He and E.Y. Yuan, New double soft emission theorems, Phys. Rev. D 92 (2015) 065030 [arXiv:1503.04816] [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].
Y.-t. Huang and C. Wen, Soft theorems from anomalous symmetries, JHEP 12 (2015) 143 [arXiv:1509.07840] [INSPIRE].
J. Rao and B. Feng, Note on identities inspired by new soft theorems, JHEP 04 (2016) 173 [arXiv:1604.00650] [INSPIRE].
F. Cachazo, P. Cha and S. Mizera, Extensions of theories from soft limits, JHEP 06 (2016) 170 [arXiv:1604.03893] [INSPIRE].
A.P. Saha, Double soft theorem for perturbative gravity, JHEP 09 (2016) 165 [arXiv:1607.02700] [INSPIRE].
A. Luna, S. Melville, S.G. Naculich and C.D. White, Next-to-soft corrections to high energy scattering in QCD and gravity, JHEP 01 (2017) 052 [arXiv:1611.02172] [INSPIRE].
C. Cheung, K. Kampf, J. Novotny, C.-H. Shen and J. Trnka, A periodic table of effective field theories, JHEP 02 (2017) 020 [arXiv:1611.03137] [INSPIRE].
H. Elvang, C.R.T. Jones and S.G. Naculich, Soft photon and graviton theorems in effective field theory, Phys. Rev. Lett. 118 (2017) 231601 [arXiv:1611.07534] [INSPIRE].
A.P. Saha, Double soft theorem for perturbative gravity II: some details on CHY soft limits, arXiv:1702.02350 [INSPIRE].
M. Ademollo et al., Soft dilations and scale renormalization in dual theories, Nucl. Phys. B 94 (1975) 221 [INSPIRE].
J.A. Shapiro, On the renormalization of dual models, Phys. Rev. D 11 (1975) 2937 [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].
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].
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].
S.G. Avery and B.U.W. Schwab, Burg-Metzner-Sachs symmetry, string theory and soft theorems, Phys. Rev. D 93 (2016) 026003 [arXiv:1506.05789] [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 tree-level string amplitudes, arXiv:1601.03457 [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. 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].
A. Strominger and A. Zhiboedov, Gravitational memory, BMS supertranslations and soft theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].
M. Campiglia and A. Laddha, Asymptotic symmetries of gravity and soft theorems for massive particles, JHEP 12 (2015) 094 [arXiv:1509.01406] [INSPIRE].
M. Campiglia and A. Laddha, Sub-subleading soft gravitons: new symmetries of quantum gravity?, Phys. Lett. B 764 (2017) 218 [arXiv:1605.09094] [INSPIRE].
E. Conde and P. Mao, BMS supertranslations and not so soft gravitons, JHEP 05 (2017) 060 [arXiv:1612.08294] [INSPIRE].
T. He, D. Kapec, A.-M. Raclariu and A. Strominger, Loop-corrected virasoro symmetry of 4D quantum gravity, arXiv:1701.00496 [INSPIRE].
M. Campiglia and A. Laddha, Sub-subleading soft gravitons and large diffeomorphisms, JHEP 01 (2017) 036 [arXiv:1608.00685] [INSPIRE].
M. Asorey, A.P. Balachandran, F. Lizzi and G. Marmo, Equations of motion as constraints: superselection rules, ward identities, JHEP 03 (2017) 136 [arXiv:1612.05886] [INSPIRE].
C. de Lacroix, H. Erbin, S.P. Kashyap, A. Sen and M. Verma, Closed superstring field theory and its applications, arXiv:1703.06410 [INSPIRE].
F.E. Low, Bremsstrahlung of very low-energy quanta in elementary particle collisions, Phys. Rev. 110 (1958) 974 [INSPIRE].
A. Sen and B. Zwiebach, A proof of local background independence of classical closed string field theory, Nucl. Phys. B 414 (1994) 649 [hep-th/9307088] [INSPIRE].
A. Sen and B. Zwiebach, Quantum background independence of closed string field theory, Nucl. Phys. B 423 (1994) 580 [hep-th/9311009] [INSPIRE].
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ArXiv ePrint: 1702.03934
Harish-Chandra Research Institute is a Constituent Unit of the Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India.
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Sen, A. Soft theorems in superstring theory. J. High Energ. Phys. 2017, 113 (2017). https://doi.org/10.1007/JHEP06(2017)113
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DOI: https://doi.org/10.1007/JHEP06(2017)113