Built on

P. Tourkine, Integrands and loop momentum in string and field theory, Phys. Rev. D 102
Original
1901
Earlier work this paper cites.
S. Mizera, Aspects of Scattering Amplitudes and Moduli Space Localization , Ph.D. thesis , Princeton, Inst. Advanced Study (2020a), arXiv:1906.02099 [hep-th]
Original
1906
Earlier work this paper cites.
Y. Geyer, R. Monteiro, and R. Stark-Muchão, Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality, JHEP 12
Original
1908
Earlier work this paper cites.
Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, The Duality Between Color and Kinematics and its Applications, (2019), arXiv:1909.01358 [hep-th]
Original
1909
Earlier work this paper cites.
E. Casali, S. Mizera, and P. Tourkine, Monodromy relations from twisted homology, JHEP 12
Original
1910
Earlier work this paper cites.
S. Mizera, Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes, Phys. Rev. Lett. 124
Original
1912
Earlier work this paper cites.
J. Igusa, Modular Forms and Projective Invariants, Amer. J. Math. 89
1967
Earlier work this paper cites.
G. Veneziano, Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cim. A 57
1968
Earlier work this paper cites.
M. B. Green and J. H. Schwarz, Supersymmetrical String Theories, Phys. Lett. B 109
1982
Earlier work this paper cites.
J. H. Schwarz, Superstring Theory, Phys. Rept. 89
1982
Earlier work this paper cites.
M. B. Green, J. H. Schwarz, and L. Brink, N=4 Yang-Mills and N=8 Supergravity as Limits of String Theories, Nucl. Phys. B198
1982
Earlier work this paper cites.
H. Kawai, D. C. Lewellen, and S. H. H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B269
1986
Earlier work this paper cites.
S. Tsuyumine, On Siegel modular forms of degree three, Amer. J. Math. 108
1986
Earlier work this paper cites.
M. B. Green, J. H. Schwarz, and E. Witten, SUPERSTRING THEORY. VOL. 1: INTRODUCTION , Cambridge Monographs on Mathematical Physics (1988)
1988
Earlier work this paper cites.
E. D’Hoker and D. H. Phong, The Geometry of String Perturbation Theory, Rev. Mod. Phys. 60
1988
Earlier work this paper cites.
E. D’Hoker and D. H. Phong, Conformal Scalar Fields and Chiral Splitting on Superriemann Surfaces, Commun. Math. Phys. 125
1989
Earlier work this paper cites.
A. Tsuchiya, More on One Loop Massless Amplitudes of Superstring Theories, Phys. Rev. D39
1989
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, M. Perelstein, and J. S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B530
1998
Earlier work this paper cites.
E. D’Hoker and D. H. Phong, Lectures on two loop superstrings, Superstring theory. Proceedings, International Conference, Hangzhou, P.R. China, August 12-15, 2002 , Conf. Proc. C0208124
2002
Earlier work this paper cites.
N. Berkovits, ICTP lectures on covariant quantization of the superstring, ICTP Lect. Notes Ser. 13
2003
Earlier work this paper cites.

Similar

E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun.Math.Phys. 252
2004
Cited alongside, same era.
R. Roiban, M. Spradlin, and A. Volovich, On the tree level S matrix of Yang-Mills theory, Phys.Rev. D70
2004
Cited alongside, same era.
E. Casali, S. Mizera, and P. Tourkine, Loop amplitudes monodromy relations and color-kinematics duality, JHEP 03
Original
2005
Cited alongside, same era.
E. D’Hoker, M. Gutperle, and D. H. Phong, Two-loop superstrings and S-duality, Nucl. Phys. B722
2005
Cited alongside, same era.
A. Edison, S. He, O. Schlotterer, and F. Teng, One-loop Correlators and BCJ Numerators from Forward Limits, JHEP 09
Original
2005
Cited alongside, same era.

Then

S. Grushevsky and R. Salvati Manni, The superstring cosmological constant and the Schottky form in genus 5, Am. J. Math. 133
Original
2011
Later among the works it cites.
A. G. Tsuchiya, On the pole structures of the disconnected part of hyper elliptic g loop M point super string amplitudes, (2012), arXiv:1209.6117 [hep-th]
Original
2012
Later among the works it cites.
Z. Bern, J. J. M. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban, Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes, Phys. Rev. D 85
Original
2012
Later among the works it cites.
E. D’Hoker and M. B. Green, Zhang-Kawazumi Invariants and Superstring Amplitudes, (2013), arXiv:1308.4597 [hep-th]
Original
2013
Later among the works it cites.
C. R. Mafra, O. Schlotterer, and S. Stieberger, Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation, Nucl. Phys. B873

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2021

Superstring loop amplitudes from the field theory limit

Geyer, Yvonne, Monteiro, Ricardo, Stark-Muchão, Ricardo

Understand

We propose a procedure to determine the moduli-space integrands of loop-level superstring amplitudes for massless external states in terms of the field theory limit.

We focus on the type II superstring.
The procedure is to: (i) take a supergravity loop integrand written in a BCJ double-copy representation, (ii) use the loop-level scattering equations to translate that integrand into the ambitwistor string moduli-space integrand, localised on the nodal Riemann sphere, and (iii) uplift that formula to one on the higher-genus surface valid for the superstring, guided by modular invariance.
We show how this works for the four-point amplitude at two loops, where we reproduce the known answer, and at three loops, where we present a conjecture that is consistent with a previous proposal for the chiral measure.

Built on

P. Tourkine, Integrands and loop momentum in string and field theory, Phys. Rev. D 102
Original
1901
Earlier work this paper cites.
S. Mizera, Aspects of Scattering Amplitudes and Moduli Space Localization , Ph.D. thesis , Princeton, Inst. Advanced Study (2020a), arXiv:1906.02099 [hep-th]
Original
1906
Earlier work this paper cites.
Y. Geyer, R. Monteiro, and R. Stark-Muchão, Two-Loop Scattering Amplitudes: Double-Forward Limit and Colour-Kinematics Duality, JHEP 12
Original
1908
Earlier work this paper cites.
Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, The Duality Between Color and Kinematics and its Applications, (2019), arXiv:1909.01358 [hep-th]
Original
1909
Earlier work this paper cites.
E. Casali, S. Mizera, and P. Tourkine, Monodromy relations from twisted homology, JHEP 12
Original
1910
Earlier work this paper cites.
S. Mizera, Kinematic Jacobi Identity is a Residue Theorem: Geometry of Color-Kinematics Duality for Gauge and Gravity Amplitudes, Phys. Rev. Lett. 124
Original
1912
Earlier work this paper cites.
J. Igusa, Modular Forms and Projective Invariants, Amer. J. Math. 89
1967
Earlier work this paper cites.
G. Veneziano, Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories, Nuovo Cim. A 57
1968
Earlier work this paper cites.
M. B. Green and J. H. Schwarz, Supersymmetrical String Theories, Phys. Lett. B 109
1982
Earlier work this paper cites.
J. H. Schwarz, Superstring Theory, Phys. Rept. 89
1982
Earlier work this paper cites.
M. B. Green, J. H. Schwarz, and L. Brink, N=4 Yang-Mills and N=8 Supergravity as Limits of String Theories, Nucl. Phys. B198
1982
Earlier work this paper cites.
H. Kawai, D. C. Lewellen, and S. H. H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B269
1986
Earlier work this paper cites.
S. Tsuyumine, On Siegel modular forms of degree three, Amer. J. Math. 108
1986
Earlier work this paper cites.
M. B. Green, J. H. Schwarz, and E. Witten, SUPERSTRING THEORY. VOL. 1: INTRODUCTION , Cambridge Monographs on Mathematical Physics (1988)
1988
Earlier work this paper cites.
E. D’Hoker and D. H. Phong, The Geometry of String Perturbation Theory, Rev. Mod. Phys. 60
1988
Earlier work this paper cites.
E. D’Hoker and D. H. Phong, Conformal Scalar Fields and Chiral Splitting on Superriemann Surfaces, Commun. Math. Phys. 125
1989
Earlier work this paper cites.
A. Tsuchiya, More on One Loop Massless Amplitudes of Superstring Theories, Phys. Rev. D39
1989
Earlier work this paper cites.
Z. Bern, L. J. Dixon, D. C. Dunbar, M. Perelstein, and J. S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B530
1998
Earlier work this paper cites.
E. D’Hoker and D. H. Phong, Lectures on two loop superstrings, Superstring theory. Proceedings, International Conference, Hangzhou, P.R. China, August 12-15, 2002 , Conf. Proc. C0208124
2002
Earlier work this paper cites.
N. Berkovits, ICTP lectures on covariant quantization of the superstring, ICTP Lect. Notes Ser. 13
2003
Earlier work this paper cites.

Similar

E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun.Math.Phys. 252
2004
Cited alongside, same era.
R. Roiban, M. Spradlin, and A. Volovich, On the tree level S matrix of Yang-Mills theory, Phys.Rev. D70
2004
Cited alongside, same era.
E. Casali, S. Mizera, and P. Tourkine, Loop amplitudes monodromy relations and color-kinematics duality, JHEP 03
Original
2005
Cited alongside, same era.
E. D’Hoker, M. Gutperle, and D. H. Phong, Two-loop superstrings and S-duality, Nucl. Phys. B722
2005
Cited alongside, same era.
A. Edison, S. He, O. Schlotterer, and F. Teng, One-loop Correlators and BCJ Numerators from Forward Limits, JHEP 09
Original
2005
Cited alongside, same era.