Abstract
The pure spinor formalism for the superstring was recently obtained by gauge-fixing a purely bosonic classical action involving a twistor-like constraint ∂xm(γ m λ) α = 0 where λα is a d=10 pure spinor. This twistor-like constraint replaces the usual Virasoro constraint ∂xm∂x m = 0, and the Green-Schwarz fermionic spacetime spinor variables θα arise as Faddeev-Popov ghosts for this constraint.
In this paper, the purely bosonic classical action is simplified by replacing the classical d=10 pure spinor λα with a d=10 projective pure spinor. The pure spinor and Green-Schwarz formalisms for the superparticle and superstring are then obtained as different gauge-fixings of this purely bosonic classical action, and the Green-Schwarz kappa symmetry is directly related to the pure spinor BRST symmetry. Since a d=10 projective pure spinor parameterizes \( \frac{\mathrm{SO}(10)}{\mathrm{U}(5)} \), this action can be interpreted as a standard ĉ = 5 topological action where one integrates over the \( \frac{\mathrm{SO}(10)}{\mathrm{U}(5)} \) choice of complex structure. Finally, a purely bosonic action for the d=11 supermembrane is proposed which reduces upon double-dimensional reduction to the purely bosonic action for the d=10 Type IIA superstring.
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References
N. Berkovits, Pure spinors, twistors and emergent supersymmetry, JHEP 12 (2012) 006 [arXiv:1105.1147] [INSPIRE].
N. Berkovits, Twistor Origin of the Superstring, JHEP 03 (2015) 122 [arXiv:1409.2510] [INSPIRE].
E. Witten, Twistor-Like Transform in Ten-Dimensions, Nucl. Phys. B 266 (1986) 245 [INSPIRE].
P.S. Howe, Pure spinors lines in superspace and ten-dimensional supersymmetric theories, Phys. Lett. B 258 (1991) 141 [Addendum ibid. B 259 (1991) 511] [INSPIRE].
A.K.H. Bengtsson, I. Bengtsson, M. Cederwall and N. Linden, Particles, Superparticles and Twistors, Phys. Rev. D 36 (1987) 1766 [INSPIRE].
E. Sokatchev, Harmonic superparticle, Class. Quant. Grav. 4 (1987) 237 [INSPIRE].
D.P. Sorokin, V.I. Tkach and D.V. Volkov, Superparticles, Twistors and Siegel Symmetry, Mod. Phys. Lett. A 4 (1989) 901 [INSPIRE].
N. Berkovits, A Supertwistor Description of the Massless Superparticle in Ten-dimensional Superspace, Phys. Lett. B 247 (1990) 45 [INSPIRE].
M. Tonin, World sheet supersymmetric formulations of Green-Schwarz superstrings, Phys. Lett. B 266 (1991) 312 [INSPIRE].
N. Berkovits, The Heterotic Green-Schwarz superstring on an N=(2,0) superworldsheet, Nucl. Phys. B 379 (1992) 96 [hep-th/9201004] [INSPIRE].
F. Delduc, A. Galperin, P.S. Howe and E. Sokatchev, A twistor formulation of the heterotic D = 10 superstring with manifest (8,0) world sheet supersymmetry, Phys. Rev. D 47 (1993) 578 [hep-th/9207050] [INSPIRE].
E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171] [INSPIRE].
N. Berkovits, An alternative string theory in twistor space for N = 4 super Yang-Mills, Phys. Rev. Lett. 93 (2004) 011601 [hep-th/0402045] [INSPIRE].
L. Mason and D. Skinner, Ambitwistor strings and the scattering equations, JHEP 07 (2014) 048 [arXiv:1311.2564] [INSPIRE].
N. Berkovits, Infinite Tension Limit of the Pure Spinor Superstring, JHEP 03 (2014) 017 [arXiv:1311.4156] [INSPIRE].
N. Berkovits, Pure spinor formalism as an N = 2 topological string, JHEP 10 (2005) 089 [hep-th/0509120] [INSPIRE].
N. Berkovits, Towards covariant quantization of the supermembrane, JHEP 09 (2002) 051 [hep-th/0201151] [INSPIRE].
E. Bergshoeff, E. Sezgin and P.K. Townsend, Supermembranes and Eleven-Dimensional Supergravity, Phys. Lett. B 189 (1987) 75 [INSPIRE].
M. Cederwall, B.E.W. Nilsson and D. Tsimpis, Spinorial cohomology and maximally supersymmetric theories, JHEP 02 (2002) 009 [hep-th/0110069] [INSPIRE].
M. Cederwall, D = 11 supergravity with manifest supersymmetry, Mod. Phys. Lett. A 25 (2010) 3201 [arXiv:1001.0112] [INSPIRE].
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ArXiv ePrint: 1503.03080
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Berkovits, N. Origin of the pure spinor and Green-Schwarz formalisms. J. High Energ. Phys. 2015, 91 (2015). https://doi.org/10.1007/JHEP07(2015)091
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DOI: https://doi.org/10.1007/JHEP07(2015)091