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MHV amplitudes and BCFW recursion for Yang-Mills theory in the de Sitter static patch

Published 17 May 2021 in hep-th and gr-qc | (2105.07572v3)

Abstract: We study the scattering problem in the static patch of de Sitter space, i.e. the problem of field evolution between the past and future horizons of a de Sitter observer. We formulate the problem in terms of off-shell fields in Poincare coordinates. This is especially convenient for conformal theories, where the static patch can be viewed as a flat causal diamond, with one tip at the origin and the other at timelike infinity. As an important example, we consider Yang-Mills theory at tree level. We find that static-patch scattering for Yang-Mills is subject to BCFW-like recursion relations. These can reduce any static-patch amplitude to one with N{-1}MHV helicity structure, dressed by ordinary Minkowski amplitudes. We derive all the N{-1}MHV static-patch amplitudes from self-dual Yang-Mills field solutions. Using the recursion relations, we then derive from these an infinite set of MHV amplitudes, with arbitrary number of external legs.

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References (42)
  1. J. M. Maldacena, “Non-Gaussian features of primordial fluctuations in single field inflationary models,” JHEP 0305, 013 (2003) doi:10.1088/1126-6708/2003/05/013 [astro-ph/0210603]
  2. J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys.  38, 1113 (1999) [Adv. Theor. Math. Phys.  2, 231 (1998)] doi:10.1023/A:1026654312961 [hep-th/9711200].
  3. S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B 428, 105-114 (1998) doi:10.1016/S0370-2693(98)00377-3 [arXiv:hep-th/9802109 [hep-th]].
  4. E. Witten, “Anti-de Sitter space and holography,” Adv. Theor. Math. Phys.  2, 253 (1998) [hep-th/9802150].
  5. O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, “Large N field theories, string theory and gravity,” Phys. Rept.  323, 183 (2000) doi:10.1016/S0370-1573(99)00083-6 [hep-th/9905111].
  6. D. Anninos, S. A. Hartnoll and D. M. Hofman, “Static Patch Solipsism: Conformal Symmetry of the de Sitter Worldline,” Class. Quant. Grav. 29, 075002 (2012) doi:10.1088/0264-9381/29/7/075002 [arXiv:1109.4942 [hep-th]].
  7. I. F. Halpern and Y. Neiman, “Holography and quantum states in elliptic de Sitter space,” JHEP 12, 057 (2015) doi:10.1007/JHEP12(2015)057 [arXiv:1509.05890 [hep-th]].
  8. A. David, N. Fischer and Y. Neiman, “Spinor-helicity variables for cosmological horizons in de Sitter space,” Phys. Rev. D 100, no.4, 045005 (2019) doi:10.1103/PhysRevD.100.045005 [arXiv:1906.01058 [hep-th]].
  9. E. Albrychiewicz and Y. Neiman, “Scattering in the static patch of de Sitter space,” [arXiv:2012.13584 [hep-th]].
  10. M. A. Vasiliev, “Higher spin gauge theories in four-dimensions, three-dimensions, and two-dimensions,” Int. J. Mod. Phys. D 5, 763 (1996) [hep-th/9611024].
  11. M. A. Vasiliev, “Higher spin gauge theories: Star product and AdS space,” In *Shifman, M.A. (ed.): The many faces of the superworld* 533-610 [hep-th/9910096].
  12. I. R. Klebanov and A. M. Polyakov, “AdS dual of the critical O(N) vector model,” Phys. Lett. B 550, 213 (2002) [hep-th/0210114].
  13. E. Sezgin and P. Sundell, “Massless higher spins and holography,” Nucl. Phys. B 644, 303-370 (2002) [erratum: Nucl. Phys. B 660, 403-403 (2003)] doi:10.1016/S0550-3213(02)00739-3 [arXiv:hep-th/0205131 [hep-th]].
  14. E. Sezgin and P. Sundell, “Holography in 4D (super) higher spin theories and a test via cubic scalar couplings,” JHEP 07, 044 (2005) doi:10.1088/1126-6708/2005/07/044 [arXiv:hep-th/0305040 [hep-th]].
  15. S. Giombi and X. Yin, “The Higher Spin/Vector Model Duality,” J. Phys. A 46, 214003 (2013) doi:10.1088/1751-8113/46/21/214003 [arXiv:1208.4036 [hep-th]].
  16. D. Anninos, T. Hartman and A. Strominger, “Higher Spin Realization of the dS/CFT Correspondence,” Class. Quant. Grav.  34, no. 1, 015009 (2017) doi:10.1088/1361-6382/34/1/015009 [arXiv:1108.5735 [hep-th]].
  17. Y. Neiman, “Higher-spin gravity as a theory on a fixed (anti) de Sitter background,” JHEP 1504, 144 (2015) doi:10.1007/JHEP04(2015)144 [arXiv:1502.06685 [hep-th]].
  18. F. A. Berends and W. T. Giele, “Recursive Calculations for Processes with n Gluons,” Nucl. Phys. B 306, 759-808 (1988) doi:10.1016/0550-3213(88)90442-7
  19. S. J. Parke and T. R. Taylor, “An Amplitude for n𝑛nitalic_n Gluon Scattering,” Phys. Rev. Lett. 56, 2459 (1986) doi:10.1103/PhysRevLett.56.2459
  20. W. A. Bardeen, “Selfdual Yang-Mills theory, integrability and multiparton amplitudes,” Prog. Theor. Phys. Suppl. 123, 1-8 (1996) doi:10.1143/PTPS.123.1
  21. D. Cangemi, “Selfdual Yang-Mills theory and one loop like - helicity QCD multi - gluon amplitudes,” Nucl. Phys. B 484, 521-537 (1997) doi:10.1016/S0550-3213(96)00586-X [arXiv:hep-th/9605208 [hep-th]].
  22. V. E. Korepin and T. Oota, “Scattering of plane waves in selfdual Yang-Mills theory,” J. Phys. A 29, L625-L628 (1996) doi:10.1088/0305-4470/29/24/003 [arXiv:hep-th/9608064 [hep-th]].
  23. A. A. Rosly and K. G. Selivanov, “On amplitudes in selfdual sector of Yang-Mills theory,” Phys. Lett. B 399, 135-140 (1997) doi:10.1016/S0370-2693(97)00268-2 [arXiv:hep-th/9611101 [hep-th]].
  24. R. Britto, F. Cachazo and B. Feng, “New recursion relations for tree amplitudes of gluons,” Nucl. Phys. B 715, 499-522 (2005) doi:10.1016/j.nuclphysb.2005.02.030 [arXiv:hep-th/0412308 [hep-th]].
  25. R. Britto, F. Cachazo, B. Feng and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,” Phys. Rev. Lett. 94, 181602 (2005) doi:10.1103/PhysRevLett.94.181602 [arXiv:hep-th/0501052 [hep-th]].
  26. J. M. Maldacena and G. L. Pimentel, “On graviton non-Gaussianities during inflation,” JHEP 1109, 045 (2011) doi:10.1007/JHEP09(2011)045 [arXiv:1104.2846 [hep-th]].
  27. C. Armstrong, A. E. Lipstein and J. Mei, “Color/Kinematics Duality in AdS44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT,” JHEP 02, 194 (2021) doi:10.1007/JHEP02(2021)194 [arXiv:2012.02059 [hep-th]].
  28. B. Nagaraj and D. Ponomarev, “Spinor-Helicity Formalism for Massless Fields in AdS44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT,” Phys. Rev. Lett. 122, no.10, 101602 (2019) doi:10.1103/PhysRevLett.122.101602 [arXiv:1811.08438 [hep-th]].
  29. B. Nagaraj and D. Ponomarev, “Spinor-helicity formalism for massless fields in AdS44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT. Part II. Potentials,” JHEP 06, 068 (2020) doi:10.1007/JHEP06(2020)068 [arXiv:1912.07494 [hep-th]].
  30. B. Nagaraj and D. Ponomarev, “Spinor-helicity formalism for massless fields in AdS44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT III: contact four-point amplitudes,” JHEP 08, no.08, 012 (2020) doi:10.1007/JHEP08(2020)012 [arXiv:2004.07989 [hep-th]].
  31. S. Albayrak and S. Kharel, “Towards the higher point holographic momentum space amplitudes,” JHEP 02, 040 (2019) doi:10.1007/JHEP02(2019)040 [arXiv:1810.12459 [hep-th]].
  32. S. Raju, “New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators,” Phys. Rev. D 85, 126009 (2012) doi:10.1103/PhysRevD.85.126009 [arXiv:1201.6449 [hep-th]].
  33. S. Raju, “Four Point Functions of the Stress Tensor and Conserved Currents in AdS44{}_{4}start_FLOATSUBSCRIPT 4 end_FLOATSUBSCRIPT/CFT33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT,” Phys. Rev. D 85, 126008 (2012) doi:10.1103/PhysRevD.85.126008 [arXiv:1201.6452 [hep-th]].
  34. S. Albayrak, C. Chowdhury and S. Kharel, “New relation for Witten diagrams,” JHEP 10, 274 (2019) doi:10.1007/JHEP10(2019)274 [arXiv:1904.10043 [hep-th]].
  35. D. G. Boulware and L. S. Brown, “Tree Graphs and Classical Fields,” Phys. Rev. 172, 1628-1631 (1968) doi:10.1103/PhysRev.172.1628
  36. Z. Bern, J. J. M. Carrasco and H. Johansson, “New Relations for Gauge-Theory Amplitudes,” Phys. Rev. D 78, 085011 (2008) doi:10.1103/PhysRevD.78.085011 [arXiv:0805.3993 [hep-ph]].
  37. S. Albayrak, S. Kharel and D. Meltzer, “On duality of color and kinematics in (A)dS momentum space,” JHEP 03, 249 (2021) doi:10.1007/JHEP03(2021)249 [arXiv:2012.10460 [hep-th]].
  38. R. R. Metsaev, “S matrix approach to massless higher spins theory. 2: The Case of internal symmetry,” Mod. Phys. Lett. A 6, 2411-2421 (1991) doi:10.1142/S0217732391002839
  39. R. R. Metsaev, “Poincare invariant dynamics of massless higher spins: Fourth order analysis on mass shell,” Mod. Phys. Lett. A 6, 359-367 (1991) doi:10.1142/S0217732391000348
  40. D. Ponomarev and E. D. Skvortsov, “Light-Front Higher-Spin Theories in Flat Space,” J. Phys. A 50, no.9, 095401 (2017) doi:10.1088/1751-8121/aa56e7 [arXiv:1609.04655 [hep-th]].
  41. E. D. Skvortsov, T. Tran and M. Tsulaia, “Quantum Chiral Higher Spin Gravity,” Phys. Rev. Lett. 121, no.3, 031601 (2018) doi:10.1103/PhysRevLett.121.031601 [arXiv:1805.00048 [hep-th]].
  42. E. Skvortsov, T. Tran and M. Tsulaia, “More on Quantum Chiral Higher Spin Gravity,” Phys. Rev. D 101, no.10, 106001 (2020) doi:10.1103/PhysRevD.101.106001 [arXiv:2002.08487 [hep-th]].
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