Abstract
We derive an explicit formula for factorizing an n-point closed string amplitude into open string amplitudes. Our results are phrased in terms of a momentum kernel which in the limit of infinite string tension reduces to the corresponding field theory kernel. The same momentum kernel encodes the monodromy relations which lead to the minimal basis of color-ordered amplitudes in Yang-Mills theory. There are interesting consequences of the momentum kernel pertaining to soft limits of amplitudes. We also comment on surprising links between gravity and certain combinations of kinematic and color factors in gauge theory.
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H. Kawai, D.C. Lewellen and S.H. Henry Tye, A relation between tree amplitudes of closed and open strings, Nucl. Phys. B 269 (1986) 1 [SPIRES].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, B. Feng and T. Sondergaard, Gravity and Yang-Mills amplitude relations, Phys. Rev. D 82 (2010) 107702 [arXiv:1005.4367] [SPIRES].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, B. Feng and T. Sondergaard, Proof of gravity and Yang-Mills amplitude relations, JHEP 09 (2010) 067 [arXiv:1007.3111] [SPIRES].
Z. Bern, L.J. Dixon, M. Perelstein and J.S. Rozowsky, Multi-leg one-loop gravity amplitudes from gauge theory, Nucl. Phys. B 546 (1999) 423 [hep-th/9811140] [SPIRES].
Z. Bern, J.J.M. Carrasco and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [SPIRES].
T. Sondergaard, New relations for gauge-theory amplitudes with matter, Nucl. Phys. B 821 (2009) 417 [arXiv:0903.5453] [SPIRES].
Y. Jia, R. Huang and C.-Y. Liu, U(1)-decoupling, KK and BCJ relations in \( \mathcal{N} = 4 \) SYM, Phys. Rev. D 82 (2010) 065001 [arXiv:1005.1821] [SPIRES].
N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal basis for gauge theory amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [SPIRES].
S. Stieberger, Open & closed vs. pure open string disk amplitudes, arXiv:0907.2211 [SPIRES].
E. Plahte, Symmetry properties of dual tree-graph N-point amplitudes, Nuovo Cim. A 66 (1970) 713 [SPIRES].
B. Feng, R. Huang and Y. Jia, Gauge amplitude identities by on-shell recursion relation in S-matrix program, arXiv:1004.3417 [SPIRES].
Z. Bern, A. De Freitas and H.L. Wong, On the coupling of gravitons to matter, Phys. Rev. Lett. 84 (2000) 3531 [hep-th/9912033] [SPIRES].
C.R. Mafra, Simplifying the tree-level superstring massless five-point amplitude, JHEP 01 (2010) 007 [arXiv:0909.5206] [SPIRES].
S.H. Henry Tye and Y. Zhang, Dual identities inside the gluon and the graviton scattering amplitudes, JHEP 06 (2010) 071 [arXiv:1003.1732] [SPIRES].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, T. Sondergaard and P. Vanhove, Monodromy and Jacobi-like relations for color-ordered amplitudes, JHEP 06 (2010) 003 [arXiv:1003.2403] [SPIRES].
C. Cheung, D. O’Connell and B. Wecht, BCFW recursion relations and string theory, JHEP 09 (2010) 052 [arXiv:1002.4674] [SPIRES].
R.H. Boels, D. Marmiroli and N.A. Obers, On-shell recursion in string theory, JHEP 10 (2010) 034 [arXiv:1002.5029] [SPIRES].
Z. Bern, T. Dennen, Y.-T. Huang and M. Kiermaier, Gravity as the square of gauge theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693] [SPIRES].
D. Vaman and Y.-P. Yao, Constraints and generalized gauge transformations on tree-level gluon and graviton amplitudes, JHEP 11 (2010) 028 [arXiv:1007.3475] [SPIRES].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [SPIRES].
P. Vanhove, The critical ultraviolet behaviour of \( \mathcal{N} = 8 \) supergravity amplitudes, arXiv:1004.1392 [SPIRES].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, B. Feng and T. Sondergaard, New identities among gauge theory amplitudes, Phys. Lett. B 691 (2010) 268 [arXiv:1006.3214] [SPIRES].
S.H. Tye and Y. Zhang, Comment on the identities of the gluon tree amplitudes, arXiv:1007.0597 [SPIRES].
B. Feng and S. He, KLT and new relations for \( \mathcal{N} = 8 \) SUGRA and \( \mathcal{N} = 4 \) SYM, JHEP 09 (2010) 043 [arXiv:1007.0055] [SPIRES].
B. Feng, S. He, R. Huang and Y. Jia, Note on new KLT relations, JHEP 10 (2010) 109 [arXiv:1008.1626] [SPIRES].
H. Elvang and M. Kiermaier, Stringy KLT relations, global symmetries and E 7(7) violation, JHEP 10 (2010) 108 [arXiv:1007.4813] [SPIRES].
V.S. Dotsenko and V.A. Fateev, Conformal algebra and multipoint correlation functions in 2D statistical models, Nucl. Phys. B 240 (1984) 312 [SPIRES].
V.S. Dotsenko and V.A. Fateev, Four point correlation functions and the operator algebra in the two-dimensional conformal invariant theories with the central charge C < 1, Nucl. Phys. B 251 (1985) 691 [SPIRES].
S. Weinberg, Infrared photons and gravitons, Phys. Rev. 140 (1965) B516 [SPIRES].
F.A. Berends and W.T. Giele, Multiple soft gluon radiation in parton processes, Nucl. Phys. B 313 (1989) 595 [SPIRES].
V. Del Duca, A. Frizzo and F. Maltoni, Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit, Nucl. Phys. B 568 (2000) 211 [hep-ph/9909464] [SPIRES].
V. Del Duca, L.J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level, Nucl. Phys. B 571 (2000) 51 [hep-ph/9910563] [SPIRES].
R. Kleiss and H. Kuijf, Multi-gluon cross-sections and five jet production at hadron colliders, Nucl. Phys. B 312 (1989) 616 [SPIRES].
M. Kiermaier, Gravity as the square of gauge theory, talk given at Amplitudes 2010, Queen Mary University, London U.K. May 4–7 2010.
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Bjerrum-Bohr, N.E.J., Damgaard, P.H., Søndergaard, T. et al. The momentum kernel of gauge and gravity theories. J. High Energ. Phys. 2011, 1 (2011). https://doi.org/10.1007/JHEP01(2011)001
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DOI: https://doi.org/10.1007/JHEP01(2011)001