Abstract
A b-ghost was constructed for the D = 11 non-minimal pure spinor superparticle by requiring that {Q, b} = T where \( Q={\Lambda}^{\alpha }{D}_{\alpha }+{R}^{\alpha }{\overline{W}}_{\alpha } \) is the usual non-minimal pure spinor BRST operator. As was done for the D = 10 b-ghost, we will show that the D = 11 b-ghost can be simplified by introducing an SO(10, 1) fermionic vector \( {\overline{\Sigma}}^i \) constructed out of the fermionic spinor D α and pure spinor variables. This simplified version will be shown to satisfy {Q, b} = T and {b, b} = BRST - trivial.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Berkovits, Towards covariant quantization of the supermembrane, JHEP 09 (2002) 051 [hep-th/0201151] [INSPIRE].
P.S. Howe, Pure spinors, function superspaces and supergravity theories in ten-dimensions and eleven-dimensions, Phys. Lett. B 273 (1991) 90 [INSPIRE].
M.B. Green, M. Gutperle and H.H. Kwon, Light cone quantum mechanics of the eleven-dimensional superparticle, JHEP 08 (1999) 012 [hep-th/9907155] [INSPIRE].
M. Cederwall, B.E.W. Nilsson and D. Tsimpis, Spinorial cohomology and maximally supersymmetric theories, JHEP 02 (2002) 009 [hep-th/0110069] [INSPIRE].
N. Berkovits, Pure spinor formalism as an N = 2 topological string, JHEP 10 (2005) 089 [hep-th/0509120] [INSPIRE].
M. Cederwall, Towards a manifestly supersymmetric action for 11-dimensional supergravity, JHEP 01 (2010) 117 [arXiv:0912.1814] [INSPIRE].
M. Cederwall, D = 11 supergravity with manifest supersymmetry, Mod. Phys. Lett. A 25 (2010) 3201 [arXiv:1001.0112] [INSPIRE].
T. Kugo and I. Ojima, Local covariant operator formalism of non-Abelian gauge theories and quark confinement problem, Prog. Theor. Phys. Suppl. 66 (1979) 1 [INSPIRE].
M. Cederwall and A. Karlsson, Loop amplitudes in maximal supergravity with manifest supersymmetry, JHEP 03 (2013) 114 [arXiv:1212.5175] [INSPIRE].
A. Karlsson, Ultraviolet divergences in maximal supergravity from a pure spinor point of view, JHEP 04 (2015) 165 [arXiv:1412.5983] [INSPIRE].
N. Berkovits, Dynamical twisting and the b ghost in the pure spinor formalism, JHEP 06 (2013) 091 [arXiv:1305.0693] [INSPIRE].
N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 09 (2001) 016 [hep-th/0105050] [INSPIRE].
L. Brink and J.H. Schwarz, Quantum superspace, Phys. Lett. B 100 (1981) 310 [INSPIRE].
N. Berkovits, ICTP lectures on covariant quantization of the superstring, in Superstrings and related matters. Proceedings, Spring School, Trieste Italy, 18–26 March 2002, pg. 57 [ICTP Lect. Notes Ser. 13 (2003) 57] [hep-th/0209059] [INSPIRE].
O.A. Bedoya and N. Berkovits, GGI lectures on the pure spinor formalism of the superstring, in New perspectives in string theory workshop, Arcetri Florence Italy, 6 April–19 June 2009 [arXiv:0910.2254] [INSPIRE].
J. Bjornsson and M.B. Green, 5 loops in 24/5 dimensions, JHEP 08 (2010) 132 [arXiv:1004.2692] [INSPIRE].
J. Bjornsson, Multi-loop amplitudes in maximally supersymmetric pure spinor field theory, JHEP 01 (2011) 002 [arXiv:1009.5906] [INSPIRE].
R. Lipinski Jusinskas, Nilpotency of the b ghost in the non-minimal pure spinor formalism, JHEP 05 (2013) 048 [arXiv:1303.3966] [INSPIRE].
N. Berkovits and O. Chandía, Simplified pure spinor b ghost in a curved heterotic superstring background, JHEP 06 (2014) 001 [arXiv:1403.2429] [INSPIRE].
A. Karlsson, Pure spinor indications of ultraviolet finiteness in D = 4 maximal supergravity, arXiv:1506.07505 [INSPIRE].
U. Gran, GAMMA: a Mathematica package for performing gamma matrix algebra and Fierz transformations in arbitrary dimensions, hep-th/0105086 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1703.05116
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Berkovits, N., Guillen, M. Simplified D = 11 pure spinor b ghost. J. High Energ. Phys. 2017, 115 (2017). https://doi.org/10.1007/JHEP07(2017)115
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2017)115