Fetching the paper…
Reading the bibliography…
The coefficient of the $D^6 {\cal R}^4$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be proportional to the integral of the Zhang-Kawazumi (ZK) invariant over the moduli space of genus-two Riemann surfaces.
C.L. Siegel, “Symplectic Geometry”, Am. J. Math. Vol 65 (1943) pp. 1-86
1943
Earlier work this paper cites.
H. Maass, “Die Differentialgleichungen in der Theorie der Siegelschen Modulfunktionen”, Math. Annalen, Bd. 126 (1953) 44-68
1953
Earlier work this paper cites.
Erhard Gottschling, “Explizite Bestimmung der Randflchen des Fundamentalbereiches der Modulgruppe zweiten Grades, ” Math. Ann. 138 (1959), 103Ð124
1959
Earlier work this paper cites.
D. Zagier “The Rankin-Selberg method for automorphic functions which are not of rapid decay,” J. Fac. Sci. Tokyo 28 (1982) 415-438
1982
Earlier work this paper cites.
E. P. Verlinde and H. L. Verlinde, “Chiral Bosonization, Determinants and the String Partition Function,” Nucl. Phys. B 288
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.
H. Klingen, Introductory Lectures to Siegel Modular Forms
1990
Earlier work this paper cites.
R. Wentworth “The Asymptotics of the Arakelov-Green’s Function and Faltings’ Delta Invariant”, Commun. Math. Phys. 137, 427-459 (1991)
1991
Earlier work this paper cites.
C. M. Hull and P. K. Townsend, “Unity of superstring dualities,” Nucl. Phys. B 438
1995
Earlier work this paper cites.
M. B. Green and M. Gutperle, “Effects of D instantons,” Nucl. Phys. B 498
1997
Earlier work this paper cites.
M. B. Green, M. Gutperle and P. Vanhove, “One loop in eleven-dimensions,” Phys. Lett. B 409
1997
Earlier work this paper cites.
E. Kiritsis and B. Pioline, “On R**4 threshold corrections in IIb string theory and (p, q) string instantons,” Nucl. Phys. B 508
1997
Earlier work this paper cites.
ÊB. Pioline, Ê“A Note on nonperturbative R**4 couplings,” ÊPhys. Lett. B 431
1998
Earlier work this paper cites.
N. A. Obers and B. Pioline, “U duality and M theory,” Phys. Rept. 318
1999
Cited alongside, same era.
M. B. Green and S. Sethi, “Supersymmetry constraints on type IIB supergravity,” Phys. Rev.x D 59
1999
Cited alongside, same era.
M. B. Green, H. -h. Kwon and P. Vanhove, “Two loops in eleven-dimensions,” Phys. Rev. D 61
2000
Cited alongside, same era.
N. A. Obers and B. Pioline, “Eisenstein series and string thresholds,” Commun. Math. Phys. 209
2000
Cited alongside, same era.
M. B. Green and P. Vanhove, “The Low-energy expansion of the one loop type II superstring amplitude,” Phys. Rev. D 61
2000
Cited alongside, same era.
A. Frizzo, L. Magnea and R. Russo, “Scalar field theory limits of bosonic string amplitudes,” Nucl. Phys. B 579
E. D’Hoker, M. Gutperle and D. H. Phong, “Two-loop superstrings and S-duality,” Nucl. Phys. B 722
2005
Later among the works it cites.
M.B. Green and P. Vanhove, “Duality and higher derivative terms in M theory”, JHEP 0601
2006
Later among the works it cites.
N. Berkovits and C. R. Mafra, “Equivalence of two-loop superstring amplitudes in the pure spinor and RNS formalisms,” Phys. Rev. Lett. 96
2006
Later among the works it cites.
A. Basu, “The D**4 R**4 term in type IIB string theory on T**2 and U-duality,” Phys. Rev. D 77
2008
Later among the works it cites.
A. Basu, “The D**6 R**4 term in type IIB string theory on T**2 and U-duality,” Phys. Rev. D 77
2008
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2000
Cited alongside, same era.
E. D’Hoker and D. H. Phong, “Two loop superstrings. 1. Main formulas,” Phys. Lett. B 529
2002
Cited alongside, same era.
E. D’Hoker and D. H. Phong, “Lectures on two loop superstrings,” Conf. Proc. C 0208124
2002
Cited alongside, same era.
A. Sinha, “The G ^ 4 λ 16 \hat{G}^{4}\lambda^{16} term in IIB supergravity,” JHEP 0208
2002
Cited alongside, same era.
E. D’Hoker and D. H. Phong, “Two loop superstrings. 2. The Chiral measure on moduli space,” Nucl. Phys. B 636
2002
Cited alongside, same era.
E. D’Hoker and D. H. Phong, “Two loop superstrings 4: The Cosmological constant and modular forms,” Nucl. Phys. B 639
2002
Cited alongside, same era.
E. D’Hoker and D. H. Phong, “Two-loop superstrings VI: Non-renormalization theorems and the 4-point function,” Nucl. Phys. B 715
2005
Cited alongside, same era.
2008
Later among the works it cites.
2008
Later among the works it cites.
2008
Later among the works it cites.
2010
Later among the works it cites.
2010
Later among the works it cites.
2010
Later among the works it cites.
B. Pioline, “R**4 couplings and automorphic unipotent representations,” JHEP 1003
2010
Later among the works it cites.
2012
Later among the works it cites.