Fetching the paper…
Reading the bibliography…
We obtain T--duality invariant second order differential equations satisfied by the $D^8\mathcal{R}^4$ and $D^{10} \mathcal{R}^4$ interactions from the low energy expansion of the one loop four graviton amplitude in toroidally compactified type II string theory.
M. B. Green and J. H. Schwarz, “Supersymmetrical String Theories,” Phys.Lett
1982
Earlier work this paper cites.
D. Zagier, “The Rankin-Selberg method for automorphic functions which are not of rapid decay,” J. Fac. Sci. Tokyo
1982
Earlier work this paper cites.
B. McClain and B. D. B. Roth, “Modular Invariance for Interacting Bosonic Strings at Finite Temperature,” Commun. Math. Phys
1987
Earlier work this paper cites.
K. H. O’Brien and C. I. Tan, “Modular Invariance of Thermopartition Function and Global Phase Structure of Heterotic String,” Phys. Rev
1987
Earlier work this paper cites.
P. Ditsas and E. G. Floratos, “Finite Temperature Closed Bosonic String in a Finite Volume,” Phys. Lett
1988
Earlier work this paper cites.
M. B. Green and M. Gutperle, “Effects of D-instantons,” Nucl. Phys
1997
Earlier work this paper cites.
M. B. Green, M. Gutperle, and P. Vanhove, “One loop in eleven dimensions,” Phys. Lett
1997
Earlier work this paper cites.
E. Kiritsis and B. Pioline, “On R 4 R^{4} threshold corrections in type IIB string theory and (p,q) string instantons,” Nucl. Phys
1997
Earlier work this paper cites.
M. B. Green and S. Sethi, “Supersymmetry constraints on type IIB supergravity,” Phys. Rev
1999
Earlier work this paper cites.
M. B. Green, H.-h. Kwon, and P. Vanhove, “Two loops in eleven dimensions,” Phys. Rev
2000
Earlier work this paper cites.
M. B. Green and P. Vanhove, “The Low-energy expansion of the one loop type II superstring amplitude,” Phys.Rev
2000
Earlier work this paper cites.
N. A. Obers and B. Pioline, “Eisenstein series and string thresholds,” Commun. Math. Phys
2000
Earlier work this paper cites.
E. D’Hoker and D. H. Phong, “Two-loop superstrings VI: Non-renormalization theorems and the 4-point function,” Nucl. Phys
2005
Cited alongside, same era.
E. D’Hoker, M. Gutperle, and D. H. Phong, “Two-loop superstrings and S-duality,” Nucl. Phys
2005
Cited alongside, same era.
N. Berkovits and C. R. Mafra, “Equivalence of two-loop superstring amplitudes in the pure spinor and RNS formalisms,” Phys. Rev. Lett
2006
Cited alongside, same era.
M. B. Green and P. Vanhove, “Duality and higher derivative terms in M theory,” JHEP
2006
Cited alongside, same era.
N. Berkovits, “New higher-derivative R 4 R^{4} theorems,” Phys.Rev.Lett
2007
Cited alongside, same era.
A. Basu, “The D 4 R 4 D^{4}R^{4} term in type IIB string theory on T 2 T^{2} and U- duality,” Phys. Rev
Z. Bern, J. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban, “The Ultraviolet Behavior of N=8 Supergravity at Four Loops,” Phys.Rev.Lett
2009
Later among the works it cites.
M. B. Green, J. G. Russo, and P. Vanhove, “Automorphic properties of low energy string amplitudes in various dimensions,” Phys. Rev
2010
Later among the works it cites.
A. Basu, “Supersymmetry constraints on the R 4 R^{4} multiplet in type IIB on T 2 T^{2} ,” Class.Quant.Grav
2011
Later among the works it cites.
H. Gomez and C. R. Mafra, “The closed-string 3-loop amplitude and S-duality,” JHEP
2013
Later among the works it cites.
A. Basu, “The structure of the ℛ 8 \mathcal{R}^{8} term in type IIB string theory,” Class.Quant.Grav
2013
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2008
Cited alongside, same era.
A. Basu, “The D 6 R 4 D^{6}R^{4} term in type IIB string theory on T 2 T^{2} and U- duality,” Phys. Rev
2008
Cited alongside, same era.
M. B. Green, J. G. Russo, and P. Vanhove, “Modular properties of two-loop maximal supergravity and connections with string theory,” JHEP
2008
Cited alongside, same era.
A. Basu and S. Sethi, “Recursion Relations from Space-time Supersymmetry,” JHEP
2008
Cited alongside, same era.
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
2008
Cited alongside, same era.
Z. Bern, J. Carrasco, L. J. Dixon, H. Johansson, and R. Roiban, “Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity,” Phys.Rev
2008
Cited alongside, same era.
M. B. Green, S. D. Miller, J. G. Russo, and P. Vanhove, “Eisenstein series for higher-rank groups and string theory amplitudes,” 1004.0163
Cited in the paper.
A. Basu, “The D 6 R 4 D^{6}R^{4} term from three loop maximal supergravity,” Class. Quant. Grav
2014
Later among the works it cites.
G. Bossard and V. Verschinin, “ ℰ ∇ 4 R 4 \mathcal{E}\nabla^{4}R^{4} type invariants and their gradient expansion,” JHEP
2015
Later among the works it cites.
G. Bossard and A. Kleinschmidt, “Supergravity divergences, supersymmetry and automorphic forms,” JHEP
2015
Later among the works it cites.
E. D’Hoker, M. B. Green, and P. Vanhove, “On the modular structure of the genus-one Type II superstring low energy expansion,” JHEP
2015
Later among the works it cites.
A. Basu, “Constraining non-BPS interactions from counterterms in three loop maximal supergravity,” Class.Quant.Grav
2015
Later among the works it cites.
A. Basu, “Some finite terms from ladder diagrams in three and four loop maximal supergravity,” Class. Quant. Grav
2015
Later among the works it cites.