Fetching the paper…
Reading the bibliography…
In this work, we argue that the $\alpha'\to 0$ limit of closed string theory scattering amplitudes is a tropical limit.
1923
Earlier work this paper cites.
R. P. Feynman, “Mathematical formulation of the quantum theory of electromagnetic interaction,” Phys. Rev. 80
1950
Earlier work this paper cites.
E. Gottschling, “Explizite Bestimmung der Randflächen des Fundamentalbereiches der Modulgruppe zweiten Grades,” Math. Ann. 138 103-124 (1959)
1959
Earlier work this paper cites.
P. Deligne and D. Mumford. “The irreducibility of the space of curves of given genus.” Inst. Hautes Etudes Sci. Publ. Math., (36):75–109 (1969)
1969
Earlier work this paper cites.
J. Scherk, “Zero-Slope Limit of the Dual Resonance Model,” Nucl. Phys. B 31
1971
Earlier work this paper cites.
J.D. Fay, “Theta functions on Riemann surfaces.” New York: Springer-Verlag (1973)
1973
Earlier work this paper cites.
C. Itzykson and J. B. Zuber, “Quantum Field Theory,” New York, Usa: Mcgraw-hill (1980) 705 P.(International Series In Pure and Applied Physics)
1980
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. B 198
1982
Earlier work this paper cites.
D. Mumford, “Tata lectures on theta, Vol. I.” Birkhäuser, Boston (1983)
1983
Earlier work this paper cites.
D. Friedan, E. J. Martinec and S. H. Shenker, “Conformal Invariance, Supersymmetry and String Theory,” Nucl. Phys. B 271
1986
Earlier work this paper cites.
E. Witten, “Noncommutative Geometry and String Field Theory,” Nucl. Phys. B 268
1986
Earlier work this paper cites.
E. Witten, “Interacting Field Theory of Open Superstrings,” Nucl. Phys. B 276
1986
Earlier work this paper cites.
S. B. Giddings, E. J. Martinec and E. Witten, “Modular Invariance in String Field Theory,” Phys. Lett. B 176
1986
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.
M. B. Green, J. H. Schwarz and E. Witten, “Superstring Theory. Vol. 1: Introduction”, “Superstring Theory. Vol. 2: Loop Amplitudes, Anomalies And Phenomenology,” Cambridge, Uk: Univ. Pr. (1987)
1987
Earlier work this paper cites.
E. P. Verlinde and H. L. Verlinde, “Multiloop Calculations in Covariant Superstring Theory,” Phys. Lett. B 192
1987
Earlier work this paper cites.
R. R. Metsaev and A. A. Tseytlin, “On Loop Corrections To String Theory Effective Actions,” Nucl. Phys. B 298
1988
Earlier work this paper cites.
J. A. Minahan, “One Loop Amplitudes On Orbifolds And The Renormalization Of Coupling Constants,” Nucl. Phys. B 298
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, “The Geometry of String Perturbation Theory,” Rev. Mod. Phys. 60
1988
Earlier work this paper cites.
R.C. Penner, “The decorated Teichmüller space of punctured surfaces.”, Commun. Math. Phys. 113
1988
Earlier work this paper cites.
B. Zwiebach, “Quantum Closed Strings from Minimal Area,” Mod. Phys. Lett. A 5
1990
Earlier work this paper cites.
L. J. Dixon, V. Kaplunovsky and J. Louis, “Moduli dependence of string loop corrections to gauge coupling constants,” Nucl. Phys. B 355
1991
Earlier work this paper cites.
Z. Bern and D. A. Kosower, “Efficient calculation of one loop QCD amplitudes,” Phys. Rev. Lett. 66
1991
Earlier work this paper cites.
Z. Bern and D. A. Kosower, “Color decomposition of one loop amplitudes in gauge theories,” Nucl. Phys. B 362
1991
Earlier work this paper cites.
M. Taniguchi, “On the singularity of the periods of abelian differentials with normal behavior under pinching deformation”, J. Math. Kyoto Univ., 31
1991
Earlier work this paper cites.
V. S. Kaplunovsky, “One Loop Threshold Effects in String Unification,” Nucl. Phys. B 307
1992
Earlier work this paper cites.
Z. Bern and D. A. Kosower, “The Computation of loop amplitudes in gauge theories,” Nucl. Phys. B 379
1992
Earlier work this paper cites.
M. J. Strassler, “Field theory without Feynman diagrams: One loop effective actions,” Nucl. Phys. B 385
1992
Earlier work this paper cites.
M. Kontsevich, “Intersection theory on the moduli space of curves and the matrix Airy function,” Commun. Math. Phys. 147
1992
Earlier work this paper cites.
Z. Bern, D. C. Dunbar and T. Shimada, “String based methods in perturbative gravity,” Phys. Lett. B 312
1993
Earlier work this paper cites.
B. Zwiebach, “Closed String Field Theory: Quantum Action and the B-V Master Equation,” Nucl. Phys. B 390
1993
Earlier work this paper cites.
M. G. Schmidt and C. Schubert, “Worldline Green functions for multiloop diagrams,” Phys. Lett. B 331
1994
Earlier work this paper cites.
N. Berkovits and C. Vafa, “On the Uniqueness of string theory,” Mod. Phys. Lett. A 9
1994
Earlier work this paper cites.
A. Berera, “Unitary string amplitudes,” Nucl. Phys. B 411
1994
Earlier work this paper cites.
D. C. Dunbar and P. S. Norridge, “Calculation of Graviton Scattering Amplitudes Using String Based Methods,” Nucl. Phys. B 433
1995
Earlier work this paper cites.
E. D’Hoker and D. H. Phong, “The Box graph in superstring theory,” Nucl. Phys. B 440
1995
Earlier work this paper cites.
P. Di Vecchia, L. Magnea, A. Lerda, R. Marotta and R. Russo, “Two loop scalar diagrams from string theory,” Phys. Lett. B 388
1996
Cited alongside, same era.
P. Di Vecchia, L. Magnea, A. Lerda, R. Russo and R. Marotta, “String techniques for the calculation of renormalization constants in field theory,” Nucl. Phys. B 469
1996
Cited alongside, same era.
K. Roland and H. T. Sato, “Multiloop Worldline Green Functions from String Theory,” Nucl. Phys. B 480
1996
Cited alongside, same era.
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
Cited alongside, same era.
O. Aharony, A. Hanany and B. Kol, “Webs of (P,Q) Five-Branes, Five-Dimensional Field Theories and Grid Diagrams,” JHEP 9801
1998
2009
Later among the works it cites.
2009
Later among the works it cites.
Klein, Christian and Kokotov, Alexey and Korotkin, Dmitry, “Extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of genus two Riemann surfaces” Mathematische Zeitschrift, 261
2009
Later among the works it cites.
S. Grushevsky, “Superstring scattering amplitudes in higher genus,” Commun. Math. Phys. 287
2009
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
J. Polchinski, “String theory. Vol. 1: An introduction to the bosonic string”, “String theory. Vol. 2: Superstring theory and beyond,” Cambridge, UK: Univ. Pr. (1998)
1998
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.
N. Berkovits, “Super Poincare covariant quantization of the superstring,” JHEP 0004
2000
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.
C. Schubert, “Perturbative quantum field theory in the string inspired formalism,” Phys. Rept. 355
2001
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, “Two loop superstrings. 2. The Chiral measure on moduli space,” Nucl. Phys. B 636
2002
Cited alongside, same era.
2010
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.
2010
Later among the works it cites.
2010
Later among the works it cites.
C. Schubert, “Schwinger Pair Creation of Particles and Strings,” J. Phys. Conf. Ser. 287
2011
Later among the works it cites.
2011
Later among the works it cites.
2011
Later among the works it cites.
I. Itenberg, G. Mikhalkin (2011), “Geometry in the tropical limit,” [math/1108.3111]
2011
Later among the works it cites.
2011
Later among the works it cites.
M. Baker, X. Faber, “Metric properties of the tropical Abel-Jacobi map.” J. Algebr. Comb. 33, No. 3, 349-381 (2011). [math/0905.1679]
2011
Later among the works it cites.
Mark Gross “Tropical geometry and mirror symmetry”, American Mathematical Soc. 114
2011
Later among the works it cites.
2011
Later among the works it cites.
2011
Later among the works it cites.
2011
Later among the works it cites.
R. Kallosh, “ E 7 ( 7 ) E_{7(7)} Symmetry and Finiteness of N=8 Supergravity,” JHEP 1203
2012
Later among the works it cites.
2012
Later among the works it cites.
2012
Later among the works it cites.
M. Chan, M. Melo, F. Viviani, ”Tropical Teichmüller and Siegel spaces.” (2012). [arXiv:12007.2443 [math.AG]]
2012
Later among the works it cites.
2012
Later among the works it cites.
2012
Later among the works it cites.
M. Matone, “Finite Strings From Non-Chiral Mumford Forms,” JHEP 1211
2012
Later among the works it cites.
D. Abramovich, “Moduli of algebraic and tropical curves.” (2013) [arXiv:1301.0474 [math.AG]]
2013
Closest in time.
2013
Closest in time.
2013
Closest in time.
2013
Closest in time.
2013
Closest in time.
2014
Closest in time.
B. Pioline, “Rankin-Selberg Methods for Closed String Amplitudes,” Proc. Symp. Pure Math. 88
2014
Closest in time.
2015
Closest in time.