Built on

E. D’Hoker and M. B. Green, “Absence of Irreducible Multiple Zeta-Values in Melon Modular Graph Functions”, Commun. Num. Theor. Phys. 14
Original
1904
Earlier work this paper cites.
E. D’Hoker, “Integral of two-loop modular graph functions”, JHEP 06
Original
1905
Earlier work this paper cites.
D. Zagier and F. Zerbini, “Genus-Zero and Genus-One String Amplitudes and Special Multiple Zeta Values”, Commun. Num. Theor. Phys. 14
Original
1906
Earlier work this paper cites.
E. D’Hoker and M. B. Green, “Exploring transcendentality in superstring amplitudes”, JHEP 07
Original
1906
Earlier work this paper cites.
C. R. Mafra and O. Schlotterer, “All-Order Alpha’-Expansion of One-Loop Open-String Integrals”, Phys. Rev. Lett. 124
Original
1908
Earlier work this paper cites.
C. R. Mafra and O. Schlotterer, “One-Loop Open-String Integrals from Differential Equations: All-Order α \alpha ’-expansions at n n Points”, JHEP 2003
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”, arXiv:1909.01358 [hep-th]
Original
1909
Earlier work this paper cites.
F. Brown and C. Dupont, “Single-valued integration and superstring amplitudes in genus zero”, arXiv:1910.01107 [math.NT]
Original
1910
Earlier work this paper cites.
E. Casali, S. Mizera and P. Tourkine, “Monodromy Relations from Twisted Homology”, JHEP 1912
Original
1910
Earlier work this paper cites.
J. E. Gerken, A. Kleinschmidt and O. Schlotterer, “All-order differential equations for one-loop closed-string integrals and modular graph forms”, JHEP 01
Original
1911
Earlier work this paper cites.
S. M. Chester, M. B. Green, S. S. Pufu, Y. Wang and C. Wen, “Modular Invariance in Superstring Theory from 𝒩 = 4 \mathcal{N}=4 Super-Yang Mills”, [arXiv:1912.13365 [hep-th]]
Original
1912
Earlier work this paper cites.
M. B. Green, J. H. Schwarz and L. Brink, “ 𝒩 = 4 {\mathcal{N}}\!=4 Yang-Mills and 𝒩 = 8 {\mathcal{N}}\!=8 Supergravity as Limits of String Theories”, Nucl. Phys. B 198
1982
Earlier work this paper cites.
M. B. Green and J. H. Schwarz, “Infinity Cancellations in SO(32) Superstring Theory”, Phys. Lett. 151B
1985
Earlier work this paper cites.
M. B. Green and J. H. Schwarz, “The Hexagon Gauge Anomaly in Type I Superstring Theory”, Nucl. Phys. B 255
1985
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. B 269
1986
Earlier work this paper cites.
I.M Gel’fand, “General theory of hypergeometric functions”, Soviet Math. Dokl. 33
1986
Earlier work this paper cites.
M. B. Green, J. H. Schwarz and E. Witten, “Superstring Theory. Vol. 1: Introduction”, Cambridge, Uk: Univ. Pr. (1987)
1987
Earlier work this paper cites.
C. P. Burgess and T. R. Morris, “Open and Unoriented Strings a La Polyakov”, Nucl. Phys. B 291
1987
Earlier work this paper cites.
C. P. Burgess and T. R. Morris, “Open Superstrings a La Polyakov”, Nucl. Phys. B 291
1987
Earlier work this paper cites.
V.A. Vasil’ev, I.M. Gel’fand, A.V. Zelevinskii, “General hypergeometric functions on complex Grassmannians”, Funct. Anal. Prilozhen. 21
1987
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.
Z. Bern and D. A. Kosower, “A New Approach to One Loop Calculations in Gauge Theories”, Phys. Rev. D 38
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.
J. Polchinski and E. Witten, “Evidence for Heterotic - Type I String Duality”, Nucl. Phys. B 460
1996
Earlier work this paper cites.
E. G. Gimon and J. Polchinski, “Consistency Conditions for Orientifolds and D Manifolds”, Phys. Rev. D 54
1996
Earlier work this paper cites.
I. R. Klebanov and L. Thorlacius, “The Size of P-Branes”, Phys. Lett. B 371
1996
Earlier work this paper cites.
A. Hashimoto and I. R. Klebanov, “Decay of Excited D-Branes”, Phys. Lett. B 381
1996
Earlier work this paper cites.
M. R. Garousi and R. C. Myers, “Superstring Scattering from D-Branes”, Nucl. Phys. B 475
1996
Earlier work this paper cites.
I. Antoniadis, C. Bachas, C. Fabre, H. Partouche and T. R. Taylor, “Aspects of Type I - Type II - Heterotic Triality in Four-Dimensions”, Nucl. Phys. B 489
1997
Earlier work this paper cites.
P. Di Francesco, P. Mathieu and D. Senechal, “Conformal Field Theory”, Graduate Texts in Contemporary Physics, New York: Springer-Verlag, 1997
1997
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. B 530
1998
Earlier work this paper cites.
L. Cappiello, R. Marotta, R. Pettorino and F. Pezzella, “Off-Shell Amplitudes for Nonoriented Closed Strings”, Mod. Phys. Lett. A 13
1998
Earlier work this paper cites.
A. Aldi and M. Firrotta, “Closed Superstring Moduli Tree-Level Two-Point Scattering Amplitudes in Type IIB Orientifold on T 6 / ( Z 2 × Z 2 ) T^{6}/(Z_{2}\times Z_{2}) ”, arXiv:2001.09468 [hep-th]
Original
2001
Earlier work this paper cites.

Similar

S. M. Chester and S. S. Pufu, “Far Beyond the Planar Limit in Strongly-Coupled 𝒩 = 4 \mathcal{N}=4 Sym”, arXiv:2003.08412 [hep-th]
Original
2003
Cited alongside, same era.
C. Angelantonj and A. Sagnotti, “Open Strings”, Phys. Rept. 371
2003
Cited alongside, same era.
J. E. Gerken, A. Kleinschmidt and O. Schlotterer, “Generating Series of All Modular Graph Forms from Iterated Eisenstein Integrals”, arXiv:2004.05156 [hep-th]
Original
2004
Cited alongside, same era.
Single-valued multiple polylogarithms in one variable
F. Brown · 2004
Cited alongside, same era.
F. Brown, “Single-valued hyperlogarithms and unipotent differential equations.” preprint on webpage at www.ihes.fr/
2004
Cited alongside, same era.

Then

C. R. Mafra and O. Schlotterer, “The Structure of N-Point One-Loop Open Superstring Amplitudes”, JHEP 1408
Original
2014
Later among the works it cites.
G. Bossard and A. Kleinschmidt, “Supergravity Divergences, Supersymmetry and Automorphic Forms”, JHEP 1508
Original
2015
Later among the works it cites.
B. Pioline, “ D 6 R 4 D^{6}R^{4} Amplitudes in Various Dimensions”, JHEP 1504
Original
2015
Later among the works it cites.
J. Broedel, C. R. Mafra, N. Matthes and O. Schlotterer, “Elliptic multiple zeta values and one-loop superstring amplitudes”, JHEP 1507
Original
2015
Later among the works it cites.
R. Donagi and E. Witten, “Supermoduli Space is Not Projected”, Proc. Symp. Pure Math. 90

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alphaXiv searches the wider corpus for related work and actual follow-ups.

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2020

Building blocks of closed and open string amplitudes

Vanhove, Pierre, Zerbini, Federico

Understand

In this text we review various relations between building blocks of closed and open string amplitudes at tree-level and genus one.

We explain that KLT relations between tree-level closed and open string amplitudes follow from the holomorphic factorisation of conformal correlation functions on conformal blocks.
We give a simple hands-on evaluation of the $\alpha'$-expansion of tree-level closed string amplitudes displaying the special single-valued nature of the coefficients.
We show that the same techniques can be used also at genus-one, where we give a new proof of the single-valued nature of the coefficients of 2-point closed string amplitudes.

Built on

E. D’Hoker and M. B. Green, “Absence of Irreducible Multiple Zeta-Values in Melon Modular Graph Functions”, Commun. Num. Theor. Phys. 14
Original
1904
Earlier work this paper cites.
E. D’Hoker, “Integral of two-loop modular graph functions”, JHEP 06
Original
1905
Earlier work this paper cites.
D. Zagier and F. Zerbini, “Genus-Zero and Genus-One String Amplitudes and Special Multiple Zeta Values”, Commun. Num. Theor. Phys. 14
Original
1906
Earlier work this paper cites.
E. D’Hoker and M. B. Green, “Exploring transcendentality in superstring amplitudes”, JHEP 07
Original
1906
Earlier work this paper cites.
C. R. Mafra and O. Schlotterer, “All-Order Alpha’-Expansion of One-Loop Open-String Integrals”, Phys. Rev. Lett. 124
Original
1908
Earlier work this paper cites.
C. R. Mafra and O. Schlotterer, “One-Loop Open-String Integrals from Differential Equations: All-Order α \alpha ’-expansions at n n Points”, JHEP 2003
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”, arXiv:1909.01358 [hep-th]
Original
1909
Earlier work this paper cites.
F. Brown and C. Dupont, “Single-valued integration and superstring amplitudes in genus zero”, arXiv:1910.01107 [math.NT]
Original
1910
Earlier work this paper cites.
E. Casali, S. Mizera and P. Tourkine, “Monodromy Relations from Twisted Homology”, JHEP 1912
Original
1910
Earlier work this paper cites.
J. E. Gerken, A. Kleinschmidt and O. Schlotterer, “All-order differential equations for one-loop closed-string integrals and modular graph forms”, JHEP 01
Original
1911
Earlier work this paper cites.
S. M. Chester, M. B. Green, S. S. Pufu, Y. Wang and C. Wen, “Modular Invariance in Superstring Theory from 𝒩 = 4 \mathcal{N}=4 Super-Yang Mills”, [arXiv:1912.13365 [hep-th]]
Original
1912
Earlier work this paper cites.
M. B. Green, J. H. Schwarz and L. Brink, “ 𝒩 = 4 {\mathcal{N}}\!=4 Yang-Mills and 𝒩 = 8 {\mathcal{N}}\!=8 Supergravity as Limits of String Theories”, Nucl. Phys. B 198
1982
Earlier work this paper cites.
M. B. Green and J. H. Schwarz, “Infinity Cancellations in SO(32) Superstring Theory”, Phys. Lett. 151B
1985
Earlier work this paper cites.
M. B. Green and J. H. Schwarz, “The Hexagon Gauge Anomaly in Type I Superstring Theory”, Nucl. Phys. B 255
1985
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. B 269
1986
Earlier work this paper cites.
I.M Gel’fand, “General theory of hypergeometric functions”, Soviet Math. Dokl. 33
1986
Earlier work this paper cites.
M. B. Green, J. H. Schwarz and E. Witten, “Superstring Theory. Vol. 1: Introduction”, Cambridge, Uk: Univ. Pr. (1987)
1987
Earlier work this paper cites.
C. P. Burgess and T. R. Morris, “Open and Unoriented Strings a La Polyakov”, Nucl. Phys. B 291
1987
Earlier work this paper cites.
C. P. Burgess and T. R. Morris, “Open Superstrings a La Polyakov”, Nucl. Phys. B 291
1987
Earlier work this paper cites.
V.A. Vasil’ev, I.M. Gel’fand, A.V. Zelevinskii, “General hypergeometric functions on complex Grassmannians”, Funct. Anal. Prilozhen. 21
1987
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.
Z. Bern and D. A. Kosower, “A New Approach to One Loop Calculations in Gauge Theories”, Phys. Rev. D 38
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.
J. Polchinski and E. Witten, “Evidence for Heterotic - Type I String Duality”, Nucl. Phys. B 460
1996
Earlier work this paper cites.
E. G. Gimon and J. Polchinski, “Consistency Conditions for Orientifolds and D Manifolds”, Phys. Rev. D 54
1996
Earlier work this paper cites.
I. R. Klebanov and L. Thorlacius, “The Size of P-Branes”, Phys. Lett. B 371
1996
Earlier work this paper cites.
A. Hashimoto and I. R. Klebanov, “Decay of Excited D-Branes”, Phys. Lett. B 381
1996
Earlier work this paper cites.
M. R. Garousi and R. C. Myers, “Superstring Scattering from D-Branes”, Nucl. Phys. B 475
1996
Earlier work this paper cites.
I. Antoniadis, C. Bachas, C. Fabre, H. Partouche and T. R. Taylor, “Aspects of Type I - Type II - Heterotic Triality in Four-Dimensions”, Nucl. Phys. B 489
1997
Earlier work this paper cites.
P. Di Francesco, P. Mathieu and D. Senechal, “Conformal Field Theory”, Graduate Texts in Contemporary Physics, New York: Springer-Verlag, 1997
1997
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. B 530
1998
Earlier work this paper cites.
L. Cappiello, R. Marotta, R. Pettorino and F. Pezzella, “Off-Shell Amplitudes for Nonoriented Closed Strings”, Mod. Phys. Lett. A 13
1998
Earlier work this paper cites.
A. Aldi and M. Firrotta, “Closed Superstring Moduli Tree-Level Two-Point Scattering Amplitudes in Type IIB Orientifold on T 6 / ( Z 2 × Z 2 ) T^{6}/(Z_{2}\times Z_{2}) ”, arXiv:2001.09468 [hep-th]
Original
2001
Earlier work this paper cites.

Similar

S. M. Chester and S. S. Pufu, “Far Beyond the Planar Limit in Strongly-Coupled 𝒩 = 4 \mathcal{N}=4 Sym”, arXiv:2003.08412 [hep-th]
Original
2003
Cited alongside, same era.
C. Angelantonj and A. Sagnotti, “Open Strings”, Phys. Rept. 371
2003
Cited alongside, same era.
J. E. Gerken, A. Kleinschmidt and O. Schlotterer, “Generating Series of All Modular Graph Forms from Iterated Eisenstein Integrals”, arXiv:2004.05156 [hep-th]
Original
2004
Cited alongside, same era.
Single-valued multiple polylogarithms in one variable
F. Brown · 2004
Cited alongside, same era.
F. Brown, “Single-valued hyperlogarithms and unipotent differential equations.” preprint on webpage at www.ihes.fr/
2004
Cited alongside, same era.

Then

C. R. Mafra and O. Schlotterer, “The Structure of N-Point One-Loop Open Superstring Amplitudes”, JHEP 1408
Original
2014
Later among the works it cites.
G. Bossard and A. Kleinschmidt, “Supergravity Divergences, Supersymmetry and Automorphic Forms”, JHEP 1508
Original
2015
Later among the works it cites.
B. Pioline, “ D 6 R 4 D^{6}R^{4} Amplitudes in Various Dimensions”, JHEP 1504
Original
2015
Later among the works it cites.
J. Broedel, C. R. Mafra, N. Matthes and O. Schlotterer, “Elliptic multiple zeta values and one-loop superstring amplitudes”, JHEP 1507
Original
2015
Later among the works it cites.
R. Donagi and E. Witten, “Supermoduli Space is Not Projected”, Proc. Symp. Pure Math. 90

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

J. E. Gerken, A. Kleinschmidt and O. Schlotterer, “Generating series of all modular graph forms from iterated Eisenstein integrals”, [arXiv:2004.05156 [hep-th]]

Original

2004

Cited alongside, same era.

E. Casali, S. Mizera and P. Tourkine, “Loop Amplitudes Monodromy Relations and Color-Kinematics Duality”, [arXiv:2005.05329 [hep-th]]

Original

2005

Cited alongside, same era.

M. B. Green, J. G. Russo and P. Vanhove, “Non-Renormalisation Conditions in Type II String Theory and Maximal Supergravity”, JHEP 0702

2007

Cited alongside, same era.

M. B. Green, J. G. Russo and P. Vanhove, “Ultraviolet Properties of Maximal Supergravity”, Phys. Rev. Lett. 98

2007

Cited alongside, same era.

J. Polchinski, “String theory. Vol. 1: An introduction to the bosonic string”, Cambridge University Press (2007-12-19)

2007

Cited alongside, same era.

M. R. Garousi, “Superstring Scattering from O-Planes”, Nucl. Phys. B 765

2007

Cited alongside, same era.

J. Polchinski, “String theory. Vol. 2: Superstring theory and beyond”, Cambridge University Press (2007-12-19)

2007

Cited alongside, same era.

Original

2015