Abstract
Previous attempts to determine the worldsheet origin of the pure spinor formalism were not completely successful, but introduced important concepts that seem to be connected to its fundamental structure, e.g., emergent supersymmetry and the role of reparametrization symmetry. In this work, a new proposal towards the underlying gauge theory of the pure spinor superstring is presented, based on an extension of Berkovits’ twistor-like constraint. The gauge algebra is analyzed in detail and worldsheet reparametrization is shown to be a redundant symmetry. The master action is built with a careful account of the intrinsic gauge symmetries associated with the pure spinor constraint and a consistent gauge fixing is performed. After a field redefinition, spacetime supersymmetry emerges and the resulting action describes the pure spinor superstring.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Berkovits, Super Poincare covariant quantization of the superstring, JHEP04 (2000) 018 [hep-th/0001035] [INSPIRE].
H. Gomez and C.R. Mafra, The closed-string S-loop amplitude and S-duality, JHEP10 (2013) 217 [arXiv:1308.6567] [INSPIRE].
C.R. Mafra and O. Schlotterer, Towards the n-point one-loop superstring amplitude. Part I. Pure spinors and superfield kinematics, JHEP08 (2019) 090 [arXiv:1812.10969] [INSPIRE].
C.R. Mafra and O. Schlotterer, Towards the n-point one-loop superstring amplitude. Part II. Worldsheet functions and their duality to kinematics, JHEP08 (2019) 091 [arXiv:1812.10970] [INSPIRE].
C.R. Mafra and 0. Schlotterer, Towards the n-point one-loop superstring amplitude. Part III. One-loop correlators and their double-copy structure, JHEP08 (2019) 092 [arXiv:1812.10971] [INSPIRE].
L. Mazzucato, Superstrings in AdS, Phys. Rept.521 (2012) 1 [arXiv:1104.2604] [INSPIRE].
N. Berkovits and E. Witten, Supersymmetry Breaking Effects using the Pure Spinor Formalism of the Super string, JHEP06 (2014) 127 [arXiv:1404.5346] [INSPIRE].
P. Ramond, Dual Theory for Free Fermions, Phys. Rev.D 3 (1971) 2415 [INSPIRE].
A. Neveu and J.H. Schwarz, Factorizable dual model of pions, Nucl. Phys.B 31 (1971) 86 [INSPIRE].
M.B. Green and J.H. Schwarz, Supersymmetrical Dual String Theory, Nucl. Phys.B 181 (1981) 502 [INSPIRE].
M.B. Green and J.H. Schwarz, Supersymmetrical String Theories, Phys. Lett.109B (1982) 444 [INSPIRE].
N. Berkovits and C.R. Mafra, Equivalence of two-loop superstring amplitudes in the pure spinor and RNS formalisms, Phys. Rev. Lett.96 (2006) 011602 [hep-th/0509234] [INSPIRE].
N. Berkovits, Cohomology in the pure spinor formalism for the superstring, JHEP09 (2000) 046 [hep-th/0006003] [INSPIRE].
N. Berkovits and D.Z. Marchioro, Relating the Green-Schwarz and pure spinor formalisms for the superstring, JHEP01 (2005) 018 [hep-th/0412198] [INSPIRE].
N. Berkovits and R. Lipinski Jusinskas, Light-Cone Analysis of the Pure Spinor Formalism for the Superstring, JHEP08 (2014) 102 [arXiv:1406.2290] [INSPIRE].
R.L. Jusinskas, Spectrum generating algebra for the pure spinor superstring, JHEP10 (2014) 022 [arXiv:1406.1902] [INSPIRE].
D.P. Sorokin, Superbranes and superembeddings, Phys. Rept.329 (2000) 1 [hep-th/9906142] [INSPIRE].
N. Berkovits, A Covariant Action for the Heterotic Superstring With Manifest Space-time Supersymmetry and World Sheet Superconformal Invariance, Phys. Lett.B 232 (1989) 184 [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 quanti zation of superstrings, Nucl. Phys.B 639 (2002) 182 [hep-th/0206104] [INSPIRE].
N. Berkovits, Pure spinors, twistors and emergent supersymmetry, JHEP12 (2012) 006 [arXiv:1105.1147] [INSPIRE].
N. Berkovits, Twistor Origin of the Superstring, JHEP 03 (2015) 122 [arXiv:1409.2510] [INSPIRE].
N. Berkovits, Origin of the Pure Spinor and Green-Schwar z Formalisms, JHEP07 (2015) 091 [arXiv:1503.03080] [INSPIRE].
R.L. Jusinskas, Quantization of the particle with a linear massless solution, arXiv:1808.07463 [INSPIRE].
N. Berkovits, Untwisting the pure spinor formalism to the RNS and twistor string in a fiat and AdS5 x S5background, JHEP06 (2016) 127 [arXiv:1604.04617] [INSPIRE].
N. Berkovits, Relating the RNS and pure spinor formalisms for the superstring, JHEP08 (2001) 026 [hep-th/0104247] [INSPIRE].
N. Berkovits, Pure spinor formalism as an N = 2 topological string, JHEP10 (2005) 089 [hep-th/0509120] [INSPIRE].
I. Oda and M. Tonin, Y-formalism in pure spinor quantization of superstrings, Nucl. Phys.B 727 (2005) 176 [hep-th/0505277] [INSPIRE].
J. Hoogeveen and K. Skenderis, ERST quantization of the pure spinor superstring, JHEP11 (2007) 081 [arXiv:0710.2598] [INSPIRE].
R.L. Jusinskas, Notes on the ambitwistor pure spinor string, JHEP05 (2016) 116 [arXiv:1604.02915] [INSPIRE].
N. Berkovits, Infinite Tension Limit of the Pure Spinor Superstring, JHEP03 (2014) 017 [arXiv:1311.4156] [INSPIRE].
T. Azevedo and R.L. Jusinskas, Connecting the ambitwistor and the sectorized heterotic strings, JHEP10 (2017) 216 [arXiv:1707.08840] [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: 1903.10753
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Jusinskas, R.L. Towards the underlying gauge theory of the pure spinor superstring. J. High Energ. Phys. 2019, 63 (2019). https://doi.org/10.1007/JHEP10(2019)063
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2019)063