Abstract
A covariant map between the Ramond-Neveu-Schwarz (RNS) and pure spinor formalisms for the superstring is found which transforms the RNS and pure spinor BRST operators into each other. The key ingredient is a dynamical twisting of the ten spin-half RNS fermions into five spin-one and five spin-zero fermions using bosonic pure spinors that parameterize an SO(10)/U(5) coset. The map relates massless vertex operators in the two formalisms, and gives a new description of Ramond states which does not require spin fields. An argument is proposed for relating the amplitude prescriptions in the two formalisms.
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References
E. Witten, D = 10 Superstring Theory, in proceedings of Grand Unification, Philadelphia, 1983, pg. 395.
N. Berkovits, Quantization of the superstring with manifest U(5) superPoincaré invariance, Phys. Lett. B 457 (1999) 94 [hep-th/9902099] [INSPIRE].
D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].
N. Berkovits, Relating the RNS and pure spinor formalisms for the superstring, JHEP 08 (2001) 026 [hep-th/0104247] [INSPIRE].
M. Tonin, World sheet supersymmetric formulations of Green-Schwarz superstrings, Phys. Lett. B 266 (1991) 312 [INSPIRE].
M. Matone, L. Mazzucato, I. Oda, D. Sorokin and M. Tonin, The Superembedding origin of the Berkovits pure spinor covariant quantization of superstrings, Nucl. Phys. B 639 (2002) 182 [hep-th/0206104] [INSPIRE].
D.P. Sorokin, Superbranes and superembeddings, Phys. Rept. 329 (2000) 1 [hep-th/9906142] [INSPIRE].
N. Berkovits, Explaining the Pure Spinor Formalism for the Superstring, JHEP 01 (2008) 065 [arXiv:0712.0324] [INSPIRE].
N. Berkovits, Covariant quantization of the Green-Schwarz superstring in a Calabi-Yau background, Nucl. Phys. B 431 (1994) 258 [hep-th/9404162] [INSPIRE].
L. Baulieu, Transmutation of pure 2 − D supergravity into topological 2 − D gravity and other conformal theories, Phys. Lett. B 288 (1992) 59 [hep-th/9206019] [INSPIRE].
L. Baulieu, M.B. Green and E. Rabinovici, A Unifying topological action for heterotic and type-II superstring theories, Phys. Lett. B 386 (1996) 91 [hep-th/9606080] [INSPIRE].
L. Baulieu, M.B. Green and E. Rabinovici, Superstrings from theories with N > 1 world sheet supersymmetry, Nucl. Phys. B 498 (1997) 119 [hep-th/9611136] [INSPIRE].
L. Baulieu and N. Ohta, World sheets with extended supersymmetry, Phys. Lett. B 391 (1997) 295 [hep-th/9609207] [INSPIRE].
E. Witten, private communication.
N. Nekrasov, Pure spinors, beta-gammas, super-Yang-Mills and Chern-Simons, Part 2, in KITP 2009 Lecture, http://online.kitp.ucsb.edu/online/strings09/nekrasov2/.
L. Baulieu, SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry, Phys. Lett. B 698 (2011) 63 [arXiv:1009.3893] [INSPIRE].
N. Berkovits, Dynamical twisting and the b ghost in the pure spinor formalism, JHEP 06 (2013) 091 [arXiv:1305.0693] [INSPIRE].
P.A. Grassi and S. Guttenberg, On Projections to the Pure Spinor Space, JHEP 12 (2011) 089 [arXiv:1109.2848] [INSPIRE].
S. Guttenberg, A Projection to the Pure Spinor Space, arXiv:1202.0335 [INSPIRE].
P.A. Grassi, G. Policastro, M. Porrati and P. Van Nieuwenhuizen, Covariant quantization of superstrings without pure spinor constraints, JHEP 10 (2002) 054 [hep-th/0112162] [INSPIRE].
P.A. Grassi, G. Policastro and P. van Nieuwenhuizen, On the BRST cohomology of superstrings with/without pure spinors, Adv. Theor. Math. Phys. 7 (2003) 499 [hep-th/0206216] [INSPIRE].
Y. Aisaka and Y. Kazama, A New first class algebra, homological perturbation and extension of pure spinor formalism for superstring, JHEP 02 (2003) 017 [hep-th/0212316] [INSPIRE].
Y. Aisaka and Y. Kazama, Operator mapping between RNS and extended pure spinor formalisms for superstring, JHEP 08 (2003) 047 [hep-th/0305221] [INSPIRE].
W. Siegel, Classical Superstring Mechanics, Nucl. Phys. B 263 (1986) 93 [INSPIRE].
W. Siegel, Superfields in Higher Dimensional Space-time, Phys. Lett. B 80 (1979) 220 [INSPIRE].
E. Witten, Twistor-Like Transform in Ten-Dimensions, Nucl. Phys. B 266 (1986) 245 [INSPIRE].
R. Donagi and E. Witten, Supermoduli Space Is Not Projected, arXiv:1304.7798 [INSPIRE].
E. Witten, More On Superstring Perturbation Theory, arXiv:1304.2832 [INSPIRE].
E. Witten, Superstring Perturbation Theory Revisited, arXiv:1209.5461 [INSPIRE].
N. Berkovits and N. Nekrasov, Multiloop superstring amplitudes from non-minimal pure spinor formalism, JHEP 12 (2006) 029 [hep-th/0609012] [INSPIRE].
N. Berkovits, Pure spinor formalism as an N = 2 topological string, JHEP 10 (2005) 089 [hep-th/0509120] [INSPIRE].
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ArXiv ePrint: 1312.0845
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Berkovits, N. Covariant map between Ramond-Neveu-Schwarz and pure spinor formalisms for the superstring. J. High Energ. Phys. 2014, 24 (2014). https://doi.org/10.1007/JHEP04(2014)024
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DOI: https://doi.org/10.1007/JHEP04(2014)024