Abstract
We establish the equivalence between two formulations of superstring perturbation theory, one based on integration over the supermoduli space of super Riemann surfaces (SRS), the other based on integration over the bosonic moduli space with insertions of picture changing operators (PCO) on the worldsheet and the vertical integration prescription, by showing how the latter arises from a specific construction of the supermoduli integration contour.
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References
E. D’Hoker and D.H. Phong, The Geometry of String Perturbation Theory, Rev. Mod. Phys. 60 (1988) 917 [INSPIRE].
E. Witten, Notes On Super Riemann Surfaces And Their Moduli, Pure Appl. Math. Quart. 15 (2019) 57 [arXiv:1209.2459] [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
E.P. Verlinde and H.L. Verlinde, Multiloop Calculations in Covariant Superstring Theory, Phys. Lett. B 192 (1987) 95 [INSPIRE].
J.J. Atick, G.W. Moore and A. Sen, Some Global Issues in String Perturbation Theory, Nucl. Phys. B 308 (1988) 1 [INSPIRE].
A. Sen, Off-shell Amplitudes in Superstring Theory, Fortsch. Phys. 63 (2015) 149 [arXiv:1408.0571] [INSPIRE].
A. Sen and E. Witten, Filling the gaps with PCO’s, JHEP 09 (2015) 004 [arXiv:1504.00609] [INSPIRE].
E. Witten, Notes On Supermanifolds and Integration, Pure Appl. Math. Quart. 15 (2019) 3 [arXiv:1209.2199] [INSPIRE].
R. Donagi and E. Witten, Supermoduli Space Is Not Projected, Proc. Symp. Pure Math. 90 (2015) 19 [arXiv:1304.7798] [INSPIRE].
C. de Lacroix et al., Closed Superstring Field Theory and its Applications, Int. J. Mod. Phys. A 32 (2017) 1730021 [arXiv:1703.06410] [INSPIRE].
T. Erler and S. Konopka, Vertical Integration from the Large Hilbert Space, JHEP 12 (2017) 112 [arXiv:1710.07232] [INSPIRE].
C. Wang and X. Yin, Supermoduli Space and PCOs at Genus Two, to appear.
J. Polchinski, String theory. Volume 2. Superstring theory and beyond, Cambridge University Press (2007) [INSPIRE].
N. Berkovits, Super Poincare covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035] [INSPIRE].
N. Berkovits, ICTP lectures on covariant quantization of the superstring, ICTP Lect. Notes Ser. 13 (2003) 57 [hep-th/0209059] [INSPIRE].
N. Berkovits, Covariant Map Between Ramond-Neveu-Schwarz and Pure Spinor Formalisms for the Superstring, JHEP 04 (2014) 024 [arXiv:1312.0845] [INSPIRE].
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ArXiv ePrint: 2205.01106
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Wang, C., Yin, X. On the equivalence between SRS and PCO formulations of superstring perturbation theory. J. High Energ. Phys. 2023, 139 (2023). https://doi.org/10.1007/JHEP03(2023)139
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DOI: https://doi.org/10.1007/JHEP03(2023)139