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Note on new KLT relations

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Abstract

In this short note, we present two results about KLT relations discussed in recent several papers. Our first result is the re-derivation of Mason-Skinner MHV amplitude by applying the S n−3 permutation symmetric KLT relations directly to MHV amplitude. Our second result is the equivalence proof of the newly discovered S n−2 permutation symmetric KLT relations and the well-known S n−3 permutation symmetric KLT relations. Although both formulas have been shown to be correct by BCFW recursion relations, our result is the first direct check using the regularized definition of the new formula.

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References

  1. D.I. Olive, Exploration of S-Matrix Theory, Phys. Rev. B 745 (1964) 135.

    MathSciNet  Google Scholar 

  2. G.F. Chew, The Analytic S-Matrix: A Basis for Nuclear Democracy, W.A. Benjamin Inc., New York U.S.A. (1966).

    Google Scholar 

  3. R.J. Eden, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, The Analytic S-Matrix, Cambridge Univ. Press, Cambridge U.K. (1966).

    MATH  Google Scholar 

  4. R. Britto, F. Cachazo and B. Feng, New Recursion Relations for Tree Amplitudes of Gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  5. R. Britto, F. Cachazo, B. Feng and E. Witten, Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. F. Cachazo and P. Svrček, Tree level recursion relations in general relativity, hep-th/0502160 [SPIRES].

  7. P. Benincasa, C. Boucher-Veronneau and F. Cachazo, Taming tree amplitudes in general relativity, JHEP 11 (2007) 057 [hep-th/0702032] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  8. J. Bedford, A. Brandhuber, B.J. Spence and G. Travaglini, A recursion relation for gravity amplitudes, Nucl. Phys. B 721 (2005) 98 [hep-th/0502146] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. N. Arkani-Hamed and J. Kaplan, On Tree Amplitudes in Gauge Theory and Gravity, JHEP 04 (2008) 076 [arXiv:0801.2385] [SPIRES].

    Article  MathSciNet  Google Scholar 

  10. B. Feng, J. Wang, Y. Wang and Z. Zhang, BCFW Recursion Relation with Nonzero Boundary Contribution, JHEP 01 (2010) 019 [arXiv:0911.0301] [SPIRES].

    Article  ADS  Google Scholar 

  11. B. Feng and C.-Y. Liu, A note on the boundary contribution with bad deformation in gauge theory, JHEP 07 (2010) 093 [arXiv:1004.1282] [SPIRES].

    Article  ADS  Google Scholar 

  12. P. Benincasa and F. Cachazo, Consistency Conditions on the S-matrix of Massless Particles, arXiv:0705.4305 [SPIRES].

  13. S. He and H.-b. Zhang, Consistency Conditions on S-matrix of Spin 1 Massless Particles, JHEP 07 (2010) 015 [arXiv:0811.3210] [SPIRES].

    Article  ADS  Google Scholar 

  14. P.C. Schuster and N. Toro, Constructing the Tree-Level Yang-Mills S-matrix Using Complex Factorization, JHEP 06 (2009) 079 [arXiv:0811.3207] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. 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].

    MathSciNet  ADS  Google Scholar 

  16. B. Feng, R. Huang and Y. Jia, Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program, arXiv:1004.3417 [SPIRES].

  17. 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].

    Article  MathSciNet  ADS  Google Scholar 

  18. S. Stieberger, Open & Closed vs. Pure Open String Disk Amplitudes, arXiv:0907.2211 [SP IRES].

  19. 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].

    Article  ADS  Google Scholar 

  20. 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] [SP IRES].

    Article  ADS  Google Scholar 

  21. H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes Of Closed And Open Strings, Nucl. Phys. B 269 (1986) 1 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. Z. Bern, Perturbative quantum gravity and its relation to gauge theory, Living Rev. Rel. 5 (2002) 5 [gr-qc/0206071] [SPIRES].

    MathSciNet  Google Scholar 

  23. N.E.J. Bjerrum-Bohr, P.H. Damgaard, B. Feng and T. Sondergaard, Gravity and Yang-Mills Amplitude Relations, arXiv:1005.4367 [SPIRES].

  24. 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].

    ADS  Google Scholar 

  25. B. Feng and S. He, KLT and New Relations for N = 8 SUGRA and N = 4 SYM, JHEP 09 (2010) 043 [arXiv:1007.0055] [SPIRES].

    Article  ADS  Google Scholar 

  26. 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].

    Article  ADS  Google Scholar 

  27. 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].

    Article  MathSciNet  ADS  Google Scholar 

  28. H. Tye and Y. Zhang, Comment on the Identities of the Gluon Tree Amplitudes, arXiv:1007.0597 [SPIRES].

  29. S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [SPIRES].

    Article  ADS  Google Scholar 

  30. F.A. Berends, W.T. Giele and H. Kuijf, On relations between multi -gluon and multigraviton scattering, Phys. Lett. B 211 (1988) 91 [SPIRES].

    ADS  Google Scholar 

  31. V.P. Nair, A note on MHV amplitudes for gravitons, Phys. Rev. D 71 (2005) 121701 [hep-th/0501143] [SPIRES].

    ADS  Google Scholar 

  32. J. Bedford, A. Brandhuber, B.J. Spence and G. Travaglini, A recursion relation for gravity amplitudes, Nucl. Phys. B 721 (2005) 98 [hep-th/0502146] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  33. H. Elvang and D.Z. Freedman, Note on graviton MHV amplitudes, JHEP 05 (2008) 096 [arXiv:0710.1270] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  34. L. Mason and D. Skinner, Gravity, Twistors and the MHV Formalism, Commun. Math. Phys. 294 (2010) 827 [arXiv:0808.3907] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  35. D. Nguyen, M. Spradlin, A. Volovich and C. Wen, The Tree Formula for MHV Graviton Amplitudes, JHEP 07 (2010) 045 [arXiv:0907.2276] [SPIRES].

    Article  ADS  Google Scholar 

  36. M. Spradlin, A. Volovich and C. Wen, Three Applications of a Bonus Relation for Gravity Amplitudes, Phys. Lett. B 674 (2009) 69 [arXiv:0812.4767] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  37. M. Bianchi, H. Elvang and D.Z. Freedman, Generating Tree Amplitudes in N = 4 SYM and N = 8 SG, JHEP 09 (2008) 063 [arXiv:0805.0757] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  38. J.M. Drummond, M. Spradlin, A. Volovich and C. Wen, Tree-Level Amplitudes in N = 8 Supergravity, Phys. Rev. D 79 (2009) 105018 [arXiv:0901.2363] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  39. N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, A Duality For The S Matrix, JHEP 03 (2010) 020 [arXiv:0907.5418] [SPIRES].

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Center of Mathematical Science, Zhejiang University, Hangzhou, China

    Bo Feng

  2. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Golm, Germany

    Song He

  3. Zhejiang Institute of Modern Physics, Physics Department, Zhejiang University, Hangzhou, China

    Rijun Huang & Yin Jia

  4. Kavli Institute for Theoretical Physics China, CAS, Beijing, 100190, China

    Bo Feng, Song He, Rijun Huang & Yin Jia

Authors
  1. Bo Feng
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  2. Song He
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  3. Rijun Huang
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  4. Yin Jia
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Correspondence to Yin Jia.

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ArXiv ePrint: 1008.1626

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Feng, B., He, S., Huang, R. et al. Note on new KLT relations. J. High Energ. Phys. 2010, 109 (2010). https://doi.org/10.1007/JHEP10(2010)109

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  • DOI: https://doi.org/10.1007/JHEP10(2010)109

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