Abstract
We describe a notion of “higher” Wess-Zumino-Witten-like action which is natural in the context of superstring field theories formulated in the large Hilbert space. For the open string, the action is characterized by a pair of commuting cyclic A ∞ structures together with a hierarchy of higher-form potentials analogous to the Maurer-Cartan elements which appear in the conventional Wess-Zumino-Witten action. We apply this formalism to get a better understanding of symmetries of open superstring field theory and the structure of interactions in the Ramond sector, describing an interesting connection between Ramond vertices and Feynman diagrams.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Berkovits, SuperPoincaré invariant superstring field theory, Nucl. Phys. B 450 (1995) 90 [Erratum ibid. B 459 (1996) 439] [hep-th/9503099] [INSPIRE].
N. Berkovits, Y. Okawa and B. Zwiebach, WZW-like action for heterotic string field theory, JHEP 11 (2004) 038 [hep-th/0409018] [INSPIRE].
C. de Lacroix, H. Erbin, S.P. Kashyap, A. Sen and M. Verma, Closed Superstring Field Theory and its Applications, arXiv:1703.06410 [INSPIRE].
T. Erler, Analytic solution for tachyon condensation in Berkovits‘ open superstring field theory, JHEP 11 (2013) 007 [arXiv:1308.4400] [INSPIRE].
Y. Iimori, T. Noumi, Y. Okawa and S. Torii, From the Berkovits formulation to the Witten formulation in open superstring field theory, JHEP 03 (2014) 044 [arXiv:1312.1677] [INSPIRE].
T. Erler, Y. Okawa and T. Takezaki, A ∞ structure from the Berkovits formulation of open superstring field theory, arXiv:1505.01659 [INSPIRE].
T. Erler, Relating Berkovits and A ∞ superstring field theories; small Hilbert space perspective, JHEP 10 (2015) 157 [arXiv:1505.02069] [INSPIRE].
H. Kunitomo and Y. Okawa, Complete action for open superstring field theory, PTEP 2016 (2016) 023B01 [arXiv:1508.00366] [INSPIRE].
K. Goto and H. Matsunaga, A ∞ /L ∞ structure and alternative action for WZW-like superstring field theory, JHEP 01 (2017) 022 [arXiv:1512.03379] [INSPIRE].
H. Matsunaga, Notes on the Wess-Zumino-Witten-like structure: L ∞ triplet and NS-NS superstring field theory, JHEP 05 (2017) 095 [arXiv:1612.08827] [INSPIRE].
M. Kontsevich, Deformation quantization of Poisson manifolds. 1., Lett. Math. Phys. 66 (2003) 157 [q-alg/9709040] [INSPIRE].
H. Kajiura, Noncommutative homotopy algebras associated with open strings, Rev. Math. Phys. 19 (2007) 1 [math/0306332] [INSPIRE].
M. Kroyter, Superstring field theory in the democratic picture, Adv. Theor. Math. Phys. 15 (2011) 741 [arXiv:0911.2962] [INSPIRE].
T. Erler, Relating Berkovits and A ∞ superstring field theories; large Hilbert space perspective, JHEP 02 (2016) 121 [arXiv:1510.00364] [INSPIRE].
T. Erler, S. Konopka and I. Sachs, Resolving Witten’s superstring field theory, JHEP 04 (2014) 150 [arXiv:1312.2948] [INSPIRE].
T. Erler, S. Konopka and I. Sachs, NS-NS Sector of Closed Superstring Field Theory, JHEP 08 (2014) 158 [arXiv:1403.0940] [INSPIRE].
A. Sen, Gauge Invariant 1PI Effective Superstring Field Theory: Inclusion of the Ramond Sector, JHEP 08 (2015) 025 [arXiv:1501.00988] [INSPIRE].
A. Sen, BV Master Action for Heterotic and Type II String Field Theories, JHEP 02 (2016) 087 [arXiv:1508.05387] [INSPIRE].
T. Erler, Y. Okawa and T. Takezaki, Complete Action for Open Superstring Field Theory with Cyclic A ∞ Structure, JHEP 08 (2016) 012 [arXiv:1602.02582] [INSPIRE].
T. Erler, S. Konopka and I. Sachs, One Loop Tadpole in Heterotic String Field Theory, arXiv:1704.01210 [INSPIRE].
K. Ohmori and Y. Okawa, Open superstring field theory based on the supermoduli space, arXiv:1703.08214 [INSPIRE].
E. Witten, Superstring Perturbation Theory Revisited, arXiv:1209.5461 [INSPIRE].
T. Erler, S. Konopka and I. Sachs, Ramond Equations of Motion in Superstring Field Theory, JHEP 11 (2015) 199 [arXiv:1506.05774] [INSPIRE].
T. Erler, Supersymmetry in Open Superstring Field Theory, JHEP 05 (2017) 113 [arXiv:1610.03251] [INSPIRE].
S. Konopka, The S-matrix of superstring field theory, JHEP 11 (2015) 187 [arXiv:1507.08250] [INSPIRE].
M. Kontsevich and Y. Soibelman, Homological mirror symmetry and torus fibrations, math/0011041 [INSPIRE].
H. Matsunaga, Comments on complete actions for open superstring field theory, JHEP 11 (2016) 115 [arXiv:1510.06023] [INSPIRE].
S. Konopka and I. Sachs, Open Superstring Field Theory on the Restricted Hilbert Space, JHEP 04 (2016) 164 [arXiv:1602.02583] [INSPIRE].
H. Kunitomo, Space-time supersymmetry in WZW-like open superstring field theory, PTEP 2017 (2017) 043B04 [arXiv:1612.08508] [INSPIRE].
N. Berkovits, The Ramond sector of open superstring field theory, JHEP 11 (2001) 047 [hep-th/0109100] [INSPIRE].
T. Erler, Marginal Solutions for the Superstring, JHEP 07 (2007) 050 [arXiv:0704.0930] [INSPIRE].
Y. Okawa, Analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 084 [arXiv:0704.0936] [INSPIRE].
Y. Okawa, Comments on Schnabl’s analytic solution for tachyon condensation in Witten’s open string field theory, JHEP 04 (2006) 055 [hep-th/0603159] [INSPIRE].
T. Erler and M. Schnabl, A Simple Analytic Solution for Tachyon Condensation, JHEP 10 (2009) 066 [arXiv:0906.0979] [INSPIRE].
T. Erler and C. Maccaferri, String Field Theory Solution for Any Open String Background, JHEP 10 (2014) 029 [arXiv:1406.3021] [INSPIRE].
K. Goto and H. Kunitomo, Construction of action for heterotic string field theory including the Ramond sector, JHEP 12 (2016) 157 [arXiv:1606.07194] [INSPIRE].
H. Kunitomo, Y. Okawa, H. Sukeno and T. Takezaki, Fermion scattering amplitudes from gauge-invariant actions for open superstring field theory, arXiv:1612.00777 [INSPIRE].
M. Kroyter, Y. Okawa, M. Schnabl, S. Torii and B. Zwiebach, Open superstring field theory I: gauge fixing, ghost structure and propagator, JHEP 03 (2012) 030 [arXiv:1201.1761] [INSPIRE].
S. Torii, Validity of Gauge-Fixing Conditions and the Structure of Propagators in Open Superstring Field Theory, JHEP 04 (2012) 050 [arXiv:1201.1762] [INSPIRE].
Y. Iimori and S. Torii, Relation between the Reducibility Structures and between the Master Actions in the Witten Formulation and the Berkovits Formulation of Open Superstring Field Theory, JHEP 10 (2015) 127 [arXiv:1507.08757] [INSPIRE].
H. Matsunaga, Gauge reducibility of superstring field theory and Batalin-Vilkovisky master action, arXiv:1706.00352 [INSPIRE].
E.P. Verlinde and H.L. Verlinde, Multiloop Calculations in Covariant Superstring Theory, Phys. Lett. B 192 (1987) 95 [INSPIRE].
U. Carow-Watamura, Z.F. Ezawa, K. Harada, A. Tezuka and S. Watamura, Chiral Bosonization of Superconformal Ghosts on Riemann Surface and Path Integral Measure, Phys. Lett. B 227 (1989) 73 [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: 1706.02629
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
Erler, T. Superstring field theory and the Wess-Zumino-Witten action. J. High Energ. Phys. 2017, 57 (2017). https://doi.org/10.1007/JHEP10(2017)057
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)057