Abstract
We generalize the CHY formalism to one-loop level, based on the framework of the null string theory. The null string, a tensionless string theory, produces the same results as the ones from the chiral ambitwistor string theory, with the latter believed to give a string interpretation of the CHY formalism. A key feature of our formalism is the interpretation of the modular parameters. We find that the S modular transformation invariance of the ordinary string theory does not survive in the case of the null string theory. Treating the integration over the modular parameters this way enable us to derive the n-gons scattering amplitude in field theory, thus proving the n-gons conjecture.
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References
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles in Arbitrary Dimensions, Phys. Rev. Lett. 113 (2014) 171601 [arXiv:1307.2199] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering of Massless Particles: Scalars, Gluons and Gravitons, JHEP 07 (2014) 033 [arXiv:1309.0885] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, Scattering equations and Kawai-Lewellen-Tye orthogonality, Phys. Rev. D 90 (2014) 065001 [arXiv:1306.6575] [INSPIRE].
L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, JHEP 07 (2014) 048 [arXiv:1311.2564] [INSPIRE].
E. Casali and P. Tourkine, On the null origin of the ambitwistor string, JHEP 11 (2016) 036 [arXiv:1606.05636] [INSPIRE].
T. Adamo, E. Casali and D. Skinner, Ambitwistor strings and the scattering equations at one loop, JHEP 04 (2014) 104 [arXiv:1312.3828] [INSPIRE].
Y. Geyer, L. Mason, R. Monteiro and P. Tourkine, One-loop amplitudes on the Riemann sphere, JHEP 03 (2016) 114 [arXiv:1511.06315] [INSPIRE].
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:1507.00321] [INSPIRE].
E. Casali and P. Tourkine, Infrared behaviour of the one-loop scattering equations and supergravity integrands, JHEP 04 (2015) 013 [arXiv:1412.3787] [INSPIRE].
S. He and E.Y. Yuan, One-loop Scattering Equations and Amplitudes from Forward Limit, Phys. Rev. D 92 (2015) 105004 [arXiv:1508.06027] [INSPIRE].
F. Cachazo, S. He and E.Y. Yuan, One-Loop Corrections from Higher Dimensional Tree Amplitudes, JHEP 08 (2016) 008 [arXiv:1512.05001] [INSPIRE].
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:1508.03627] [INSPIRE].
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, Phys. Rev. Lett. 116 (2016) 061601 [arXiv:1509.02169] [INSPIRE].
K. Ohmori, Worldsheet Geometries of Ambitwistor String, JHEP 06 (2015) 075 [arXiv:1504.02675] [INSPIRE].
Z. Bern and D.A. Kosower, The computation of loop amplitudes in gauge theories, Nucl. Phys. B 379 (1992) 451 [INSPIRE].
A. Karlhede and U. Lindström, The Classical Bosonic String in the Zero Tension Limit, Class. Quant. Grav. 3 (1986) L73 [INSPIRE].
U. Lindström, B. Sundborg and G. Theodoridis, The zero tension limit of the superstring, Phys. Lett. B 253 (1991) 319 [INSPIRE].
W. Siegel, Amplitudes for left-handed strings, arXiv:1512.02569 [INSPIRE].
O. Hohm, W. Siegel and B. Zwiebach, Doubled α ′ -geometry, JHEP 02 (2014) 065 [arXiv:1306.2970] [INSPIRE].
Y. Li and W. Siegel, Chiral Superstring and CHY Amplitude, arXiv:1702.07332 [INSPIRE].
F. Lizzi, B. Rai, G. Sparano and A. Srivastava, Quantization of the Null String and Absence of Critical Dimensions, Phys. Lett. B 182 (1986) 326 [INSPIRE].
J. Gamboa, C. Ramírez and M. Ruiz-Altaba, Null spinning strings, Nucl. Phys. B 338 (1990) 143 [INSPIRE].
J. Isberg, U. Lindström, B. Sundborg and G. Theodoridis, Classical and quantized tensionless strings, Nucl. Phys. B 411 (1994) 122 [hep-th/9307108] [INSPIRE].
J. Gamboa, C. Ramírez and M. Ruiz-Altaba, Quantum null (super)strings, Phys. Lett. B 225 (1989) 335 [INSPIRE].
Y.-t. Huang, W. Siegel and E.Y. Yuan, Factorization of Chiral String Amplitudes, JHEP 09 (2016) 101 [arXiv:1603.02588] [INSPIRE].
P. Francesco, P. Mathieu and D. Sénéchal, Conformal field theory, Springer Science & Business Media (2012).
M. Yu, C. Zhang and Y.-Z. Zhang, Operator formalism for null string at one loop, to appear.
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ArXiv ePrint: 1704.01290
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Yu, M., Zhang, C. & Zhang, YZ. One loop amplitude from null string. J. High Energ. Phys. 2017, 51 (2017). https://doi.org/10.1007/JHEP06(2017)051
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DOI: https://doi.org/10.1007/JHEP06(2017)051