Advertisement

Ambitwistor strings and the scattering equations at one loop

  • Tim Adamo
  • Eduardo Casali
  • David Skinner
Open Access
Article

Abstract

Ambitwistor strings are chiral, infinite tension analogues of conventional string theory whose target space is the space of complex null geodesics and whose spectrum consists exclusively of massless states. At genus zero, these strings underpin the Cachazo-He-Yuan formulæ for tree level scattering of gravitons, gluons and scalars. In this paper we extend these formulæ in a number of directions. Firstly, we consider Ramond sector vertex operators and construct simple amplitudes involving space-time fermions. These agree with tree amplitudes in ten dimensional supergravity and super Yang-Mills. We then show that, after the usual GSO projections, the ambitwistor string partition function is modular invariant. We consider the scattering equations at genus one, and calculate one loop scattering amplitudes for NS-NS external states in the Type II ambitwistor string. We conjecture that these give new representations of (the integrand of) one loop supergravity amplitudes and we show that they have the expected behaviour under factorization of the worldsheet in both non-separating and separating degenerations.

Keywords

Scattering Amplitudes Superstrings and Heterotic Strings Supergravity Models Differential and Algebraic Geometry 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, arXiv:1311.2564 [INSPIRE].
  2. [2]
    C. LeBrun, Spaces of Complex Null Geodesics in Complex Riemannanian Geometry, Trans. Amer. Math. Soc. 278 (1983) 209.CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    E. Witten, Twistor - Like Transform in Ten-Dimensions, Nucl. Phys. B 266 (1986) 245 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  4. [4]
    N. Berkovits, Infinite Tension Limit of the Pure Spinor Superstring, JHEP 03 (2014) 017 [arXiv:1311.4156] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimension, arXiv:1307.2199 [INSPIRE].
  6. [6]
    F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, arXiv:1309.0885 [INSPIRE].
  7. [7]
    L. Dolan and P. Goddard, Proof of the Formula of Cachazo, He and Yuan for Yang-Mills Tree Amplitudes in Arbitrary Dimension, arXiv:1311.5200 [INSPIRE].
  8. [8]
    D.J. Gross and P.F. Mende, The High-Energy Behavior of String Scattering Amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  9. [9]
    D.J. Gross and P.F. Mende, String Theory Beyond the Planck Scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  10. [10]
    E. Witten, Parity invariance for strings in twistor space, Adv. Theor. Math. Phys. 8 (2004) 779 [hep-th/0403199] [INSPIRE].CrossRefzbMATHMathSciNetGoogle Scholar
  11. [11]
    J. Polchinski, String Theory. Vol. 2: Superstring Theory and Beyond. Cambridge University Press, Cambridge U.K. (1998).CrossRefGoogle Scholar
  12. [12]
    E. Witten, Superstring Perturbation Theory Revisited, arXiv:1209.5461 [INSPIRE].
  13. [13]
    R.J. Baston and L.J. Mason, Conformal Gravity, the Einstein Equations and Spaces of Complex Null Geodesics, Class. Quant. Grav. 4 (1987) 815 [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  14. [14]
    T. Adamo, M. Bullimore, L. Mason and D. Skinner, Scattering Amplitudes and Wilson Loops in Twistor Space, J. Phys. A 44 (2011) 454008 [arXiv:1104.2890] [INSPIRE].ADSMathSciNetGoogle Scholar
  15. [15]
    D. Friedan, S.H. Shenker and E.J. Martinec, Covariant Quantization of Superstrings, Phys. Lett. B 160 (1985) 55 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  16. [16]
    D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  17. [17]
    V.G. Knizhnik and A.B. Zamolodchikov, Current Algebra and Wess-Zumino Model in Two-Dimensions, Nucl. Phys. B 247 (1984) 83 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  18. [18]
    C.R. Mafra, O. Schlotterer and S. Stieberger, Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation, Nucl. Phys. B 873 (2013) 419 [arXiv:1106.2645] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  19. [19]
    H. Gomez and E.Y. Yuan, N-point tree-level scattering amplitude in the new Berkovitsstring, JHEP 04 (2014) 046 [arXiv:1312.5485] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    F. Cachazo and D. Skinner, Gravity from Rational Curves in Twistor Space, Phys. Rev. Lett. 110 (2013) 161301 [arXiv:1207.0741] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    D. Skinner, Twistor Strings for N = 8 Supergravity, arXiv:1301.0868 [INSPIRE].
  22. [22]
    E. Witten, Notes On Holomorphic String And Superstring Theory Measures Of Low Genus, arXiv:1306.3621 [INSPIRE].
  23. [23]
    J. Polchinski, Factorization of Bosonic String Amplitudes, Nucl. Phys. B 307 (1988) 61 [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  24. [24]
    T. Adamo, Worldsheet factorization for twistor-strings, arXiv:1310.8602 [INSPIRE].
  25. [25]
    A. Yamada, Precise Variational Formulas for Abelian Differentials, Kodai Math. J 3 (1980) 114.CrossRefzbMATHMathSciNetGoogle Scholar
  26. [26]
    M.P. Tuite and A. Zuevsky, The Szegó Kernel on a Sewn Riemann Surface, Commun. Math. Phys. 306 (2011) 617 [arXiv:1002.4114] [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  27. [27]
    J. Fay, Theta Functions on Riemann Surfaces, Lecture Notes in Mathematics, Springer (1973).Google Scholar
  28. [28]
    E. D’Hoker and D.H. Phong, Lectures on two loop superstrings, Conf. Proc. C0208124 (2002) 85 [hep-th/0211111] [INSPIRE].Google Scholar
  29. [29]
    F. Cachazo, S. He and E.Y. Yuan, Scattering Equations and KLT Orthogonality, arXiv:1306.6575 [INSPIRE].
  30. [30]
    E. D’Hoker and D.H. Phong, Conformal Scalar Fields and Chiral Splitting on SuperRiemann Surfaces, Commun. Math. Phys. 125 (1989) 469 [INSPIRE].ADSCrossRefzbMATHMathSciNetGoogle Scholar
  31. [31]
    M.B. Green, J.H. Schwarz and L. Brink, N = 4 Yang-Mills and N = 8 Supergravity as Limits of String Theories, Nucl. Phys. B 198 (1982) 474 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    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/9811140] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  33. [33]
    E. D’Hoker and D.H. Phong, The Box graph in superstring theory, Nucl. Phys. B 440 (1995) 24 [hep-th/9410152] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  34. [34]
    M.B. Green and P. Vanhove, The Low-energy expansion of the one loop type-II superstring amplitude, Phys. Rev. D 61 (2000) 104011 [hep-th/9910056] [INSPIRE].ADSMathSciNetGoogle Scholar
  35. [35]
    M.B. Green, J.G. Russo and P. Vanhove, Low energy expansion of the four-particle genus-one amplitude in type-II superstring theory, JHEP 02 (2008) 020 [arXiv:0801.0322] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  36. [36]
    A. Hodges, New expressions for gravitational scattering amplitudes, JHEP 07 (2013) 075 [arXiv:1108.2227] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  37. [37]
    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].ADSCrossRefMathSciNetGoogle Scholar
  38. [38]
    A. Ochirov and P. Tourkine, BCJ duality and double copy in the closed string sector, arXiv:1312.1326 [INSPIRE].
  39. [39]
    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] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of Applied Mathematics & Theoretical PhysicsUniversity of CambridgeCambridgeUnited Kingdom

Personalised recommendations