Abstract
We elucidate some exact relations between light-cone and covariant string field theories on the basis of the homological perturbation lemma for A∞. The covariant string field splits into the light-cone string field and trivial excitations of BRST quartets: the latter generates the gauge symmetry and covariance. We first show that the reduction of gauge degrees can be performed by applying the lemma, which gives a refined version of the no-ghost theorem of covariant strings. Then, we demonstrate that after the reduction, gauge-fixed theory can be regarded as a kind of effective field theory and it provides an exact gauge-fixing procedure taking into account interactions. As a result, a novel light-cone string field theory is obtained from Witten’s open string field theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Witten, Noncommutative Geometry and String Field Theory, Nucl. Phys. B 268 (1986) 253 [INSPIRE].
B. Zwiebach, Closed string field theory: Quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [INSPIRE].
M. Kaku and K. Kikkawa, The Field Theory of Relativistic Strings. I. Trees, Phys. Rev. D 10 (1974) 1110 [INSPIRE].
M. Kaku and K. Kikkawa, The Field Theory of Relativistic Strings. II. Loops and Pomerons, Phys. Rev. D 10 (1974) 1823 [INSPIRE].
H. Hata, K. Itoh, T. Kugo, H. Kunitomo and K. Ogawa, Covariant String Field Theory, Phys. Rev. D 34 (1986) 2360 [INSPIRE].
H. Hata, K. Itoh, T. Kugo, H. Kunitomo and K. Ogawa, Covariant String Field Theory. 2., Phys. Rev. D 35 (1987) 1318 [INSPIRE].
T. Kugo, Covariantized Light Cone String Field Theory, In Santiago 1987, Proceedings, Quantum mechanics of fundamental systems 2, KUNS-0917, pp. 167–187, [INSPIRE].
W. Siegel and B. Zwiebach, Interacting BRST From the Light Cone, Nucl. Phys. B 299 (1988) 206 [INSPIRE].
M. Kato and K. Ogawa, Covariant Quantization of String Based on BRS Invariance, Nucl. Phys. B 212 (1983) 443 [INSPIRE].
Y. Aisaka and Y. Kazama, Relating Green-Schwarz and extended pure spinor formalisms by similarity transformation, JHEP 04 (2004) 070 [hep-th/0404141] [INSPIRE].
M. Crainic, On the perturbation lemma, and deformations, math/0403266.
A. Berglund, Homological perturbation lemma for algebra over operads, Algebr. Geom. Topol. 14 (2014) 2511 [arXiv:0909.3485].
B. Valltte, Algebra + Homotopy = Operad, [arXiv:1202.3245].
M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, (1992).
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].
H. Kajiura, Noncommutative homotopy algebras associated with open strings, Rev. Math. Phys. 19 (2007) 1 [math/0306332] [INSPIRE].
H. Kajiura, Homotopy algebra morphism and geometry of classical string field theory, Nucl. Phys. B 630 (2002) 361 [hep-th/0112228] [INSPIRE].
S. Konopka, The S-matrix of superstring field theory, JHEP 11 (2015) 187 [arXiv:1507.08250] [INSPIRE].
T. Erler, Supersymmetry in Open Superstring Field Theory, JHEP 05 (2017) 113 [arXiv:1610.03251] [INSPIRE].
M. Doubek, B. Jurčo and J. Pulmann, Quantum L ∞ Algebras and the Homological Perturbation Lemma, Commun. Math. Phys. 367 (2019) 215 [arXiv:1712.02696] [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].
T. Erler, Superstring Field Theory and the Wess-Zumino-Witten Action, JHEP 10 (2017) 057 [arXiv:1706.02629] [INSPIRE].
A. Sen, Wilsonian Effective Action of Superstring Theory, JHEP 01 (2017) 108 [arXiv:1609.00459] [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: 1901.08555
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
Matsunaga, H. Light-cone reduction of Witten’s open string field theory. J. High Energ. Phys. 2019, 143 (2019). https://doi.org/10.1007/JHEP04(2019)143
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2019)143