# 臺灣博碩士論文加值系統

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 本篇文章中將簡短的回顧散射振幅。回顧內容包含兩部分。第一部分裡，我們回顧散射振幅的定義以及旋量螺度，並且使用旋量螺度的方式來表示楊-米爾斯理論的散射振幅。在第二部分中，我們將簡短回顧超對稱。這部分的回顧僅止于使用在建構超對稱散射振幅的基本程度。在這之後我們還會介紹超重力理論。 在概覽完散射振幅的簡介以後，第三部分我們將開始尋找俱有自然性質的建構散射振幅元件。我們將會給出一套系統方式去建構散射振幅，這套模式中每一個建構元件在高能量時都俱有更好的漸進行為z^(-2)，就好比散射振幅一樣。我們將在N=7超重力理論中使用布里托、卡查索、馮以及維滕的遞迴關係，並且使用特定的動量形變以展現更好的漸進行為。並且我們將會解釋這個更好的行為是因為使用了N=8超重力理論中的附加關係式。
 We review some ideas of scattering amplitudes. The review consists of two parts. In Part I, we review the definition of scattering amplitudes and spinor helicity. We use the technology of spinor helicity to represent scattering amplitudes in Yang-Mills theory. In part II, we review supersymmetry. The review will be on a basic level to introduce superamplitudes. We then introduce supergravity amplitudes. After introducing amplitudes, we search for natural building blocks for supergravity amplitudes in part III. We want to show a systematic way to find the building blocks which are term-by-term bonus z^(-2) large momentum scaling just like amplitudes. For a given choice of deformation legs, we present such an expansion in the form of the Britto, Cachazo, Feng and Witten recursion relation in N=7 supergravity based on a special shift. We will show that this improved scaling behavior, with respect to the fully N=8 representation, is due to its automatic incorporation of the so called bonus relations.
 1 Introduction ............................................................. 3Part I2 Spinor Formalism ..................................................... 62.1 RepresentationofLorentzgroup............................... 62.2 SpinorFields .......................................................... 92.3 Yang-MillsTheory ................................................. 112.4 LittleGroup............................................................ 123 BCFW Recursion Relation ......................................... 133.1 BCFW.................................................................... 143.2 Multi-stepBCFW.................................................... 17Part II4 Supersymmetry ....................................................... 184.1 N=1Supersymmetry ............................................. 194.2 SupersymmetryWardIdentities............................... 224.3 N=4SuperYang-MillsTheory.................................. 234.4 SuperBCFW .......................................................... 254.5 N=8SupergravityAmplitudes................................. 26Part III5 Bonus scaling and BCFW in N = 7 supergravity ........ 285.1 N=7 superamplitudes............................................ 295.1.1 From N=8 to N=7 ................................................ 295.1.2 BCFW in the N=7 formalism .................................. 315.2 Bonus z scaling of N=7“badshift”BCFW terms ............. 325.2.1 A particular [-,+> test shift: NkMHV amplitudes....... 325.2.2 General [-,+> test shifts: the MHV case ...................... 355.2.3 Comparison to other formulas for supergravity amplitudes . . . . 365.3 N =8 bonus relations and N =7 bonus scaling: the MHV case . . . . . 365.4 Bonus scaling of “bad shift” BCFW for string amplitudes . . . . . . . . . 386 Conclusion and Future directions ....................................41A Derivation of P.................................................................43Reference............................................................................44
 [1] R. Britto, F. Cachazo, B. Feng and E. Witten, Phys. Rev. Lett. 94, 181602 (2005)[hep-th/0501052].[2] N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, JHEP 1003, 020 (2010) [arXiv:0907.5418 [hep-th]].[3] N. Arkani-Hamed, J. L. Bourjaily, F. Cachazo, A. B. Goncharov, A. Postnikov and J. Trnka, [arXiv:1212.5605 [hep-th]].[4] O. Aharony, O. Bergman, D. L. Jaeris and J. Maldacena, JHEP 0810, 091 (2008) [arXiv:0806.1218 [hep-th]].[5] K. Hosomichi, K. -M. Lee, S. Lee, S. Lee and J. Park, JHEP 0809, 002 (2008) [arXiv:0806.4977 [hep-th]].[6] S. Lee, Phys. Rev. Lett. 105, 151603 (2010) [arXiv:1007.4772 [hep-th]].[7] Y. -T. Huang and C. Wen, “ABJM amplitudes and the positive orthogonal Grass-mannian,” JHEP 1402, 104 (2014) [arXiv:1309.3252 [hep-th]].[8] Y. -t. Huang, C. Wen and D. Xie, “The Positive orthogonal Grassmannian and loopamplitudes of ABJM,” [arXiv:1402.1479 [hep-th]].[9] J. M. Drummond, J. M. Henn and J. Plefka, JHEP 0905, 046 (2009) [arXiv:0902.2987 [hep-th]].[10] N. Arkani-Hamed and J. Kaplan, JHEP 0804, 076 (2008) [arXiv:0801.2385 [hep-th]].[11] D. A. McGady and L. Rodina, [arXiv:1408.5125 [hep-th]].[12] N. Arkani-Hamed, F. Cachazo and J. Kaplan, JHEP 1009, 016 (2010) [arXiv:0808.1446 [hep-th]].[13] D. Nguyen, M. Spradlin, A. Volovich and C. Wen, JHEP 1007, 045 (2010) [arXiv:0907.2276 [hep-th]].[14] A. Hodges, JHEP 1307 (2013) [arXiv:1108.2227 [hep-th]].[15] H. Elvang, Y. t. Huang and C. Peng, JHEP 1109, 031 (2011) [arXiv:1102.4843[hep-th]].[16] D. Nandan and C. Wen, JHEP 1208, 040 (2012) [arXiv:1204.4841 [hep-th]].[17] R. Boels, K. J. Larsen, N. A. Obers and M. Vonk, JHEP 0811, 015 (2008) [arXiv:0808.2598 [hep-th]].[18] R. H. Boels, D. Marmiroli and N. A. Obers, JHEP 1010, 034 (2010) [arXiv:1002.5029 [hep-th]].[19] S. He, D. Nandan and C. Wen, JHEP 1102, 005 (2011) [arXiv:1011.4287 [hep-th]]. 44[20] B. Feng, K. Zhou, C. Qiao and J. Rao, JHEP 1503, 023 (2015) [arXiv:1411.0452 [hep-th]].
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 1 N=7超重力中之優化漸進表現以及BCFW

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