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These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
J. L. Gervais and B. Sakita, “Field Theory Interpretation Of Supergauges In Dual Models,” Nucl. Phys. B34
1971
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P. Ramond, “Dual Theory For Free Fermions,” Phys. Rev. D3
1971
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L. Brink, P. DiVecchia, and P. Howe, “A Locally Supersymmetric And Reparametrisation Invariant Action For The Spinning String,” Phys. Lett. 65B
1976
Earlier work this paper cites.
S. Deser and B. Zumino, “A Complete Action For The Spinning String,” Phys. Lett. B65
1976
Earlier work this paper cites.
F. Gliozzi, J. Scherk, and D. I. Olive, “Supergravity And The Dual Spinor Model,” Phys. Lett. B65
1976
Earlier work this paper cites.
P. Howe, “Super Weyl Transformations In Two Dimensions,” Journal of Physics A12
1979
Earlier work this paper cites.
M. Brown and S. J. Gates, “Superspace Geometry And 𝒩 = 1 {\mathcal{N}}=1 Nonminimal Supergravity,” Ann. Phys. (N.Y.) 122
1979
Earlier work this paper cites.
R. Bott and L. Tu, Differential Forms In Algebraic Topology
1982
Earlier work this paper cites.
E. Martinec, “Superspace Geometry Of Fermionic Strings,” Phys. Rev. D28
1983
Earlier work this paper cites.
M. B. Green and J. H. Schwarz, “Infinity Cancellations In SO(32) Superstring Theory,” Phys. Lett. B151
1984
Earlier work this paper cites.
A. Baranov and A. Schwarz, “Multiloop Contribution To String Theory,” JETP Lett. 42
1985
Earlier work this paper cites.
D. Friedan, “Notes On String Theory And Two Dimensional Conformal Field Theory,” in M. B. Green et. al., eds. Unified String Theories
1986
Earlier work this paper cites.
G. Moore, P. Nelson, and J. Polchinski, “Strings And Supermoduli,” Phys. Lett. 169B
1986
Earlier work this paper cites.
P. Nelson and G. Moore, “Heterotic Geometry,” Nucl. Phys. B274
1986
Earlier work this paper cites.
D. Friedan, E. Martinec, and S. Shenker, “Covariant Quantization Of Superstrings,” Phys. Lett. B160
1986
Earlier work this paper cites.
E. Martinec, “Nonrenormalization Theorems And Fermionic String Finiteness,” Phys. Lett. B171
1986
Earlier work this paper cites.
A. Baranov and A. Schwarz, “On The Multiloop Contribution To The String Theory,” Int. J. Mod. Phys. A2
1987
Earlier work this paper cites.
Yu. I. Manin, “Critical Dimensions of String Theories and the Dualizing Sheaf on the Moduli Space of (Super) Curves,” Funct. Anal. Appl. 20
1987
Earlier work this paper cites.
A. Baranov, Y. I. Manin, I. Frolov, and A. S. Schwarz, “A Superanalog Of The Selberg Trace Formula And Multiloop Contributions For Fermionic Strings,” Commun. Math. Phys. 111
1987
Earlier work this paper cites.
S. B. Giddings and P. C. Nelson, “The Geometry Of Superriemann Surfaces,” Comm. Math. Phys. 116
1987
Cited alongside, same era.
E. Verlinde and H. Verlinde, “Multiloop Calculations In Covariant Superstring Theory,” Phys. Lett. B192
1987
Cited alongside, same era.
E. Martinec, “Conformal Field Theory On A (Super-)Riemann Surface,” Nucl. Phys. B281
1987
Cited alongside, same era.
P. Deligne, letter to Yu. I. Manin (ca. 1987)
1987
Cited alongside, same era.
P. Deligne, letter to Yu. I. Manin (September 25, 1987)
1987
Cited alongside, same era.
A. A. Rosly, A. S. Schwarz, and A. A. Voronov, “Geometry Of Superconformal Manifolds,” Comm. Math. Phys. 119
1988
Cited alongside, same era.
P. Nelson, “Some Simple Supermoduli Spaces,” in Superstrings ’88
1989
Later among the works it cites.
V. G. Kac and J. W. van de Leur, “On Classification Of Superconformal Algebras,” in Strings 1988
1989
Later among the works it cites.
G. T. Horowitz, R. C. Myers, and S. P. Martin, “BRST Cohomology Of The Superstring At Arbitrary Ghost Number,” Phys. Lett. B218
1989
Later among the works it cites.
E. D’Hoker and D. H. Phong, “Superstrings, Super Riemann Surfaces, and Supermoduli Space,” UCLA preprint (1989), in Symposia Mathematica, String Theory, Vol XXXIII (Academic Press London and New York, 1990)
1990
Later among the works it cites.
S. N. Dolgikh, A. A. Rosly, and A. S. Schwarz, “Supermoduli Spaces,” Commun. Math. Phys. 135
1990
Later among the works it cites.
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L. Crane and J. Rabin, “Super Riemann Surfaces: Uniformization And Teichmuller Theory,” Commun. Math. Phys. 113
1988
Cited alongside, same era.
C. LeBrun and M. Rothstein, “Moduli Of Super Riemann Surfaces,” Comm. Math. Phys. 117
1988
Cited alongside, same era.
L. Alvarez-Gaumé, C. Gomez, P. C. Nelson, G. Sierra, and C. Vafa, “Fermionic Strings In The Operator Formalism,” Nucl. Phys. B311
1988
Cited alongside, same era.
E. D’Hoker and D. H. Phong, “The Geometry Of String Perturbation Theory,” Rev. Mod. Phys. 60
1988
Cited alongside, same era.
J. Cohn, “ 𝒩 = 2 {\mathcal{N}}=2 Super Riemann Surfaces,” Nucl. Phys. B284
1988
Cited alongside, same era.
M. J. Bergvelt and J. M. Rabin, “Supercurves, Their Jacobians, And Super KP Equations,” Duke. Math. J. 98
1988
Cited alongside, same era.
E. Witten, “On The Structure Of The Topological Phase Of Two-Dimensional Gravity,” Nucl. Phys. B340
1990
Later among the works it cites.
J. Rabin and P. Topiwala, “The Super Gaga Principle And Families Of Super Riemann Surfaces,” Proc. AMS 113
1991
Later among the works it cites.
S. Giddings, “Punctures On Super Riemann Surfaces,” Commun. Math. Phys. 143
1992
Later among the works it cites.
B. DeWitt, Supermanifolds
1992
Later among the works it cites.
N. Berkovits and C. Vafa, “On The Uniqueness Of String Theory,” Mod. Phys. Lett. A9
1994
Later among the works it cites.
J. M. Rabin, “Super Elliptic Curves,” J. Geom. and Phys. 15
1995
Later among the works it cites.
N. Berkovits and C. Vafa, “ N = 4 {\it N}=4 Topological Strings,” Nucl. Phys. B433
1995
Later among the works it cites.
A. Belopolsky, “De Rham Cohomology Of The Supermanifolds And Superstring BRST Cohomology,” Phys. Lett. B403
1997
Later among the works it cites.
N. Berkovits and B. Zwiebach, “On The Picture Dependence Of Ramond-Ramond Cohomology,” Nucl. Phys. B523
1998
Later among the works it cites.
P. Deligne and J. W. Morgan, “Notes On Supersymmetry (following Joseph Bernstein),” in P. Deligne et. al., eds., Quantum Fields And Strings: A Course For Mathematicians, Vol. 1
1999
Later among the works it cites.
R. Britto, F. Cachazo, and B. Feng, “Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills,” Nucl. Phys. B725
2005
Later among the works it cites.
P. Deligne, letters to E. Witten (June 21 and 22, 2010)
2010
Later among the works it cites.
P. Deligne, letter to E. Witten (March 4, 2012)
2012
Closest in time.