An algebraic approach to the scattering equations
详细信息    查看全文
  • 作者:Rijun Huang ; Junjie Rao ; Bo Feng ; Yang-Hui He
  • 关键词:Scattering Amplitudes ; Differential and Algebraic Geometry ; Gauge Symmetry
  • 刊名:Journal of High Energy Physics
  • 出版年:2015
  • 出版时间:December 2015
  • 年:2015
  • 卷:2015
  • 期:12
  • 全文大小:625 KB
  • 参考文献:[1]F. Cachazo, S. He and E.Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality, Phys. Rev. D 90 (2014) 065001 [arXiv:鈥?306.鈥?575 ] [INSPIRE ].ADS
    [2]F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:鈥?307.鈥?199 ] [INSPIRE ].CrossRef ADS
    [3]F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, JHEP 07 (2014) 033 [arXiv:鈥?309.鈥?885 ] [INSPIRE ].CrossRef ADS
    [4]F. Cachazo, S. He and E.Y. Yuan, Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations, JHEP 01 (2015) 121 [arXiv:鈥?409.鈥?256 ] [INSPIRE ].CrossRef ADS MathSciNet
    [5]F. Cachazo, S. He and E.Y. Yuan, Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM, JHEP 07 (2015) 149 [arXiv:鈥?412.鈥?479 ] [INSPIRE ].CrossRef ADS MathSciNet
    [6]D. Fairlie and D. Roberts, Dual Models without Tachyons 鈥?a New Approach, unpublished, Durham preprint PRINT-72-2440 (1972).
    [7]D. Roberts, Mathematical Structure of Dual Amplitudes, Ph.D. Thesis, Durham University, Durham U.K. (1972).
    [8]D.B. Fairlie, A Coding of Real Null Four-Momenta into World-Sheet Co-ordinates, Adv. Math. Phys. 2009 (2009) 284689 [arXiv:鈥?805.鈥?263 ] [INSPIRE ].CrossRef MathSciNet
    [9]D.J. Gross and P.F. Mende, String Theory Beyond the Planck Scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE ].CrossRef ADS MathSciNet
    [10]E. Witten, Parity invariance for strings in twistor space, Adv. Theor. Math. Phys. 8 (2004) 779 [hep-th/鈥?403199 ] [INSPIRE ].CrossRef MathSciNet MATH
    [11]P. Caputa and S. Hirano, Observations on Open and Closed String Scattering Amplitudes at High Energies, JHEP 02 (2012) 111 [arXiv:鈥?108.鈥?381 ] [INSPIRE ].CrossRef ADS MathSciNet
    [12]P. Caputa, Lightlike contours with fermions, Phys. Lett. B 716 (2012) 475 [arXiv:鈥?205.鈥?369 ] [INSPIRE ].CrossRef ADS MathSciNet
    [13]Y. Makeenko and P. Olesen, The QCD scattering amplitude from area behaved Wilson loops, Phys. Lett. B 709 (2012) 285 [arXiv:鈥?111.鈥?606 ] [INSPIRE ].CrossRef ADS
    [14]F. Cachazo, Fundamental BCJ Relation in N = 4 SYM From The Connected Formulation, arXiv:鈥?206.鈥?970 [INSPIRE ].
    [15]L. Dolan and P. Goddard, Proof of the Formula of Cachazo, He and Yuan for Yang-Mills Tree Amplitudes in Arbitrary Dimension, JHEP 05 (2014) 010 [arXiv:鈥?311.鈥?200 ] [INSPIRE ].CrossRef ADS MathSciNet
    [16]R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/鈥?412308 ] [INSPIRE ].CrossRef ADS MathSciNet
    [17]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/鈥?501052 ] [INSPIRE ].CrossRef ADS MathSciNet
    [18]L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, JHEP 07 (2014) 048 [arXiv:鈥?311.鈥?564 ] [INSPIRE ].CrossRef ADS
    [19]N. Berkovits, Infinite Tension Limit of the Pure Spinor Superstring, JHEP 03 (2014) 017 [arXiv:鈥?311.鈥?156 ] [INSPIRE ].CrossRef ADS MathSciNet
    [20]H. Gomez and E.Y. Yuan, N-point tree-level scattering amplitude in the new Berkovits鈥?string, JHEP 04 (2014) 046 [arXiv:鈥?312.鈥?485 ] [INSPIRE ].CrossRef ADS
    [21]T. Adamo, E. Casali and D. Skinner, Ambitwistor strings and the scattering equations at one loop, JHEP 04 (2014) 104 [arXiv:鈥?312.鈥?828 ] [INSPIRE ].CrossRef ADS
    [22]Y. Geyer, A.E. Lipstein and L.J. Mason, Ambitwistor Strings in Four Dimensions, Phys. Rev. Lett. 113 (2014) 081602 [arXiv:鈥?404.鈥?219 ] [INSPIRE ].CrossRef ADS
    [23]Y. Geyer, A.E. Lipstein and L. Mason, Ambitwistor strings at null infinity and (subleading) soft limits, Class. Quant. Grav. 32 (2015) 055003 [arXiv:鈥?406.鈥?462 ] [INSPIRE ].CrossRef ADS MathSciNet
    [24]E. Casali and P. Tourkine, Infrared behaviour of the one-loop scattering equations and supergravity integrands, JHEP 04 (2015) 013 [arXiv:鈥?412.鈥?787 ] [INSPIRE ].CrossRef MathSciNet
    [25]T. Adamo and E. Casali, Scattering equations, supergravity integrands and pure spinors, JHEP 05 (2015) 120 [arXiv:鈥?502.鈥?6826 ] [INSPIRE ].CrossRef ADS MathSciNet
    [26]E. Casali, Y. Geyer, L. Mason, R. Monteiro and K.A. Roehrig, New Ambitwistor String Theories, JHEP 11 (2015) 038 [arXiv:鈥?506.鈥?8771 ] [INSPIRE ].CrossRef ADS
    [27]K. Ohmori, Worldsheet Geometries of Ambitwistor String, JHEP 06 (2015) 075 [arXiv:鈥?504.鈥?2675 ] [INSPIRE ].CrossRef ADS MathSciNet
    [28]Y. Geyer, L. Mason, R. Monteiro and P. Tourkine, Loop Integrands for Scattering Amplitudes from the Riemann Sphere, Phys. Rev. Lett. 115 (2015) 121603 [arXiv:鈥?507.鈥?0321 ] [INSPIRE ].CrossRef ADS
    [29]N.E.J. Bjerrum-Bohr, P.H. Damgaard, P. Tourkine and P. Vanhove, Scattering Equations and String Theory Amplitudes, Phys. Rev. D 90 (2014) 106002 [arXiv:鈥?403.鈥?553 ] [INSPIRE ].ADS
    [30]C. Baadsgaard, N.E.J. Bjerrum-Bohr, J.L. Bourjaily and P.H. Damgaard, Integration Rules for Scattering Equations, JHEP 09 (2015) 129 [arXiv:鈥?506.鈥?6137 ] [INSPIRE ].CrossRef ADS
    [31]C. Baadsgaard, N.E.J. Bjerrum-Bohr, J.L. Bourjaily and P.H. Damgaard, Scattering Equations and Feynman Diagrams, JHEP 09 (2015) 136 [arXiv:鈥?507.鈥?0997 ] [INSPIRE ].CrossRef ADS
    [32]C. Baadsgaard, N.E.J. Bjerrum-Bohr, J.L. Bourjaily, P.H. Damgaard and B. Feng, Integration Rules for Loop Scattering Equations, JHEP 11 (2015) 080 [arXiv:鈥?508.鈥?3627 ] [INSPIRE ].CrossRef
    [33]S. He and E.Y. Yuan, One-loop Scattering Equations and Amplitudes from Forward Limit, Phys. Rev. D 92 (2015) 105004 [arXiv:鈥?508.鈥?6027 ] [INSPIRE ].ADS
    [34]C. Baadsgaard, N.E.J. Bjerrum-Bohr, J.L. Bourjaily, S. Caron-Huot, P.H. Damgaard and B. Feng, New Representations of the Perturbative S-matrix, arXiv:鈥?509.鈥?2169 [INSPIRE ].
    [35]C. Kalousios, Scattering equations, generating functions and all massless five point tree amplitudes, JHEP 05 (2015) 054 [arXiv:鈥?502.鈥?7711 ] [INSPIRE ].CrossRef ADS MathSciNet
    [36]F. Cachazo and H. Gomez, Computation of Contour Integrals on \( {\mathrm{\mathcal{M}}}_{0,n} \) , arXiv:鈥?505.鈥?3571 [INSPIRE ].
    [37]L. Dolan and P. Goddard, The Polynomial Form of the Scattering Equations, JHEP 07 (2014) 029 [arXiv:鈥?402.鈥?374 ] [INSPIRE ].CrossRef ADS MathSciNet
    [38]Y.-H. He, C. Matti and C. Sun, The Scattering Variety, JHEP 10 (2014) 135 [arXiv:鈥?403.鈥?833 ] [INSPIRE ].CrossRef ADS MathSciNet
    [39]L. Stickelberger, Ueber eine Verallgemeinerung der Kreistheilung, Math. Ann. 37 (1890) 321.CrossRef MathSciNet MATH
    [40]B. Sturmfels, Solving Systems of Polynomial Equations, Cbms Regional Conference Series in Mathematics, American Mathematical Society, Providenca U.S.A. (2002). Available online at https://鈥媘ath.鈥媌erkeley.鈥媏du/鈥媬bernd/鈥媍bms.鈥媝df .
    [41]P. Parrilo, Algebraic Techniques and Semidefinite Optimization, Massachusetts Institute of Technology: MIT OpenCourseWare, Massachusetts Institute of Technology, Cambridge U.S.A. (2006). See lecture 15.
    [42]D.R. Grayson and M.E. Stillman, Macaulay2, a software system for research in algebraic geometry. Available at http://鈥媤ww.鈥媘ath.鈥媢iuc.鈥媏du/鈥婱acaulay2/鈥?/span> .
    [43]W. Decker, G.-M. Greuel, G. Pfister and H. Schonemann, Singular 4-0-2 鈥?A computer algebra system for polynomial computations, (2015). Available at http://鈥媤ww.鈥媠ingular.鈥媢ni-kl.鈥媎e .
    [44]J. Gray, Y.-H. He, A. Ilderton and A. Lukas, STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology, Comput. Phys. Commun. 180 (2009) 107 [arXiv:鈥?801.鈥?508 ] [INSPIRE ].CrossRef ADS MathSciNet MATH
    [45]Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:鈥?805.鈥?993 ] [INSPIRE ].ADS MathSciNet
    [46]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 [INSPIRE ].CrossRef ADS MathSciNet
    [47]Z. Bern, L.J. Dixon, M. Perelstein and J.S. Rozowsky, Multileg one loop gravity amplitudes from gauge theory, Nucl. Phys. B 546 (1999) 423 [hep-th/鈥?811140 ] [INSPIRE ].CrossRef ADS MathSciNet
    [48]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:鈥?005.鈥?367 ] [INSPIRE ].ADS
    [49]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:鈥?006.鈥?214 ] [INSPIRE ].CrossRef ADS MathSciNet
    [50]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:鈥?007.鈥?111 ] [INSPIRE ].CrossRef ADS MathSciNet
    [51]S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE ].CrossRef ADS
    [52]F.A. Berends and W.T. Giele, Recursive Calculations for Processes with n Gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE ].CrossRef ADS
    [53]B. Feng, J. Rao and K. Zhou, On Multi-step BCFW Recursion Relations, JHEP 07 (2015) 058 [arXiv:鈥?504.鈥?6306 ] [INSPIRE ].CrossRef ADS MathSciNet
    [54]D.A. Kosower, Next-to-maximal helicity violating amplitudes in gauge theory, Phys. Rev. D 71 (2005) 045007 [hep-th/鈥?406175 ] [INSPIRE ].ADS MathSciNet
    [55]M.-x. Luo and C.-k. Wen, Recursion relations for tree amplitudes in super gauge theories, JHEP 03 (2005) 004 [hep-th/鈥?501121 ] [INSPIRE ]CrossRef ADS MathSciNet
  • 作者单位:Rijun Huang (1)
    Junjie Rao (1)
    Bo Feng (1) (2)
    Yang-Hui He (3) (4) (5)

    1. Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, 310027, P.R. China
    2. Center of Mathematical Science, Zhejiang University, Hangzhou, 310027, P.R. China
    3. School of Physics, NanKai University, Tianjin, 300071, P.R. China
    4. Department of Mathematics, City University, London, EC1V 0HB, U.K.
    5. Merton College, University of Oxford, Oxford, OX14JD, U.K.
  • 刊物类别:Physics and Astronomy
  • 刊物主题:Physics
    Elementary Particles and Quantum Field Theory
    Quantum Field Theories, String Theory
  • 出版者:Springer Berlin / Heidelberg
  • ISSN:1029-8479
文摘

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700