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.
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References
L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, arXiv:1311.2564 [INSPIRE].
C. LeBrun, Spaces of Complex Null Geodesics in Complex Riemannanian Geometry, Trans. Amer. Math. Soc. 278 (1983) 209.
E. Witten, Twistor - Like Transform in Ten-Dimensions, Nucl. Phys. B 266 (1986) 245 [INSPIRE].
N. Berkovits, Infinite Tension Limit of the Pure Spinor Superstring, JHEP 03 (2014) 017 [arXiv:1311.4156] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimension, arXiv:1307.2199 [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, arXiv:1309.0885 [INSPIRE].
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].
D.J. Gross and P.F. Mende, The High-Energy Behavior of String Scattering Amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].
D.J. Gross and P.F. Mende, String Theory Beyond the Planck Scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].
E. Witten, Parity invariance for strings in twistor space, Adv. Theor. Math. Phys. 8 (2004) 779 [hep-th/0403199] [INSPIRE].
J. Polchinski, String Theory. Vol. 2: Superstring Theory and Beyond. Cambridge University Press, Cambridge U.K. (1998).
E. Witten, Superstring Perturbation Theory Revisited, arXiv:1209.5461 [INSPIRE].
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].
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].
D. Friedan, S.H. Shenker and E.J. Martinec, Covariant Quantization of Superstrings, Phys. Lett. B 160 (1985) 55 [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
V.G. Knizhnik and A.B. Zamolodchikov, Current Algebra and Wess-Zumino Model in Two-Dimensions, Nucl. Phys. B 247 (1984) 83 [INSPIRE].
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].
H. Gomez and E.Y. Yuan, N-point tree-level scattering amplitude in the new Berkovits‘ string, JHEP 04 (2014) 046 [arXiv:1312.5485] [INSPIRE].
F. Cachazo and D. Skinner, Gravity from Rational Curves in Twistor Space, Phys. Rev. Lett. 110 (2013) 161301 [arXiv:1207.0741] [INSPIRE].
D. Skinner, Twistor Strings for N = 8 Supergravity, arXiv:1301.0868 [INSPIRE].
E. Witten, Notes On Holomorphic String And Superstring Theory Measures Of Low Genus, arXiv:1306.3621 [INSPIRE].
J. Polchinski, Factorization of Bosonic String Amplitudes, Nucl. Phys. B 307 (1988) 61 [INSPIRE].
T. Adamo, Worldsheet factorization for twistor-strings, arXiv:1310.8602 [INSPIRE].
A. Yamada, Precise Variational Formulas for Abelian Differentials, Kodai Math. J 3 (1980) 114.
M.P. Tuite and A. Zuevsky, The Szegó Kernel on a Sewn Riemann Surface, Commun. Math. Phys. 306 (2011) 617 [arXiv:1002.4114] [INSPIRE].
J. Fay, Theta Functions on Riemann Surfaces, Lecture Notes in Mathematics, Springer (1973).
E. D’Hoker and D.H. Phong, Lectures on two loop superstrings, Conf. Proc. C0208124 (2002) 85 [hep-th/0211111] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering Equations and KLT Orthogonality, arXiv:1306.6575 [INSPIRE].
E. D’Hoker and D.H. Phong, Conformal Scalar Fields and Chiral Splitting on SuperRiemann Surfaces, Commun. Math. Phys. 125 (1989) 469 [INSPIRE].
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].
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].
E. D’Hoker and D.H. Phong, The Box graph in superstring theory, Nucl. Phys. B 440 (1995) 24 [hep-th/9410152] [INSPIRE].
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].
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].
A. Hodges, New expressions for gravitational scattering amplitudes, JHEP 07 (2013) 075 [arXiv:1108.2227] [INSPIRE].
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].
A. Ochirov and P. Tourkine, BCJ duality and double copy in the closed string sector, arXiv:1312.1326 [INSPIRE].
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].
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Adamo, T., Casali, E. & Skinner, D. Ambitwistor strings and the scattering equations at one loop. J. High Energ. Phys. 2014, 104 (2014). https://doi.org/10.1007/JHEP04(2014)104
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DOI: https://doi.org/10.1007/JHEP04(2014)104