Abstract
We clarify a Wess-Zumino-Witten-like structure including Ramond fields and propose one systematic way to construct gauge invariant actions: Wess-Zumino-Witten-like complete action S WZW. We show that Kunitomo-Okawa’s action proposed in arXiv:1508.00366 can obtain a topological parameter dependence of Ramond fields and belongs to our WZW-like framework. In this framework, once a WZW-like functional \( {\mathcal{A}}_{\eta }={\mathcal{A}}_{\eta}\left[\Psi \right] \) of a dynamical string field Ψ is constructed, we obtain one realization of S WZW[Ψ] parametrized by Ψ. On the basis of this way, we construct an action \( \tilde{S} \) whose on-shell condition is equivalent to the Ramond equations of motion proposed in arXiv:1506.05774. Using these results, we provide the equivalence of two theories: arXiv:1508.00366 and arXiv:1506.05774.
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References
H. Kunitomo and Y. Okawa, Complete action for open superstring field theory, Prog. Theor. Exp. Phys. 2016 (2016) 023B01 [arXiv:1508.00366] [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, 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].
T. Erler, Relating Berkovits and A ∞ superstring field theories; large Hilbert space perspective, JHEP 02 (2016) 121 [arXiv:1510.00364] [INSPIRE].
K. Goto and H. Matsunaga, On-shell equivalence of two formulations for superstring field theory, arXiv:1506.06657 [INSPIRE].
S. Konopka, The S-matrix of superstring field theory, JHEP 11 (2015) 187 [arXiv:1507.08250] [INSPIRE].
A. Sen and E. Witten, Filling the gaps with PCO’s, JHEP 09 (2015) 004 [arXiv:1504.00609] [INSPIRE].
A. Sen, Supersymmetry restoration in superstring perturbation theory, JHEP 12 (2015) 075 [arXiv:1508.02481] [INSPIRE].
A. Sen, BV master action for heterotic and type II string field theories, JHEP 02 (2016) 087 [arXiv:1508.05387] [INSPIRE].
K. Goto and H. Matsunaga, A ∞ /L ∞ structure and alternative action for WZW-like superstring field theory, arXiv:1512.03379 [INSPIRE].
N. Berkovits, Super-Poincaré invariant superstring field theory, Nucl. Phys. B 450 (1995) 90 [Erratum ibid. B 459 (1996) 439] [hep-th/9503099] [INSPIRE].
N. Berkovits, A new approach to superstring field theory, Fortsch. Phys. 48 (2000) 31 [hep-th/9912121] [INSPIRE].
Y. Okawa and B. Zwiebach, Heterotic string field theory, JHEP 07 (2004) 042 [hep-th/0406212] [INSPIRE].
N. Berkovits, Y. Okawa and B. Zwiebach, WZW-like action for heterotic string field theory, JHEP 11 (2004) 038 [hep-th/0409018] [INSPIRE].
H. Matsunaga, Construction of a gauge-invariant action for type II superstring field theory, arXiv:1305.3893 [INSPIRE].
H. Matsunaga, Nonlinear gauge invariance and WZW-like action for NS-NS superstring field theory, JHEP 09 (2015) 011 [arXiv:1407.8485] [INSPIRE].
N. Berkovits, The Ramond sector of open superstring field theory, JHEP 11 (2001) 047 [hep-th/0109100] [INSPIRE].
Y. Michishita, A covariant action with a constraint and Feynman rules for fermions in open superstring field theory, JHEP 01 (2005) 012 [hep-th/0412215] [INSPIRE].
H. Kunitomo, The Ramond sector of heterotic string field theory, Prog. Theor. Exp. Phys. 2014 (2014) 043B01 [arXiv:1312.7197] [INSPIRE].
H. Kunitomo, First-order equations of motion for heterotic string field theory, Prog. Theor. Exp. Phys. 2014 (2014) 093B07 [arXiv:1407.0801] [INSPIRE].
H. Kunitomo, Symmetries and Feynman rules for the Ramond sector in open superstring field theory, Prog. Theor. Exp. Phys. 2015 (2015) 033B11 [arXiv:1412.5281] [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].
E. Witten, Interacting field theory of open superstrings, Nucl. Phys. B 276 (1986) 291 [INSPIRE].
C. Wendt, Scattering amplitudes and contact interactions in Witten’s superstring field theory, Nucl. Phys. B 314 (1989) 209 [INSPIRE].
Y. Kazama, A. Neveu, H. Nicolai and P.C. West, Symmetry structures of superstring field theories, Nucl. Phys. B 276 (1986) 366 [INSPIRE].
H. Terao and S. Uehara, Gauge invariant actions and gauge fixed actions of free superstring field theory, Phys. Lett. B 173 (1986) 134 [INSPIRE].
J.P. Yamron, A gauge invariant action for the free Ramond string, Phys. Lett. B 174 (1986) 69 [INSPIRE].
T. Kugo and H. Terao, New gauge symmetries in Witten’s Ramond string field theory, Phys. Lett. B 208 (1988) 416 [INSPIRE].
E. Witten, Noncommutative geometry and string field theory, Nucl. Phys. B 268 (1986) 253 [INSPIRE].
E. Getzler and J.D.S. Jones, A ∞ -algebras and the cyclic bar complex, Illinois J. Math. 34 (1990) 256.
M. Penkava and A.S. Schwarz, A ∞ algebras and the cohomology of moduli spaces, Trans. Amer. Math. Soc. 169 (1995) 91 [hep-th/9408064] [INSPIRE].
H. Kajiura, Noncommutative homotopy algebras associated with open strings, Rev. Math. Phys. 19 (2007) 1 [math/0306332] [INSPIRE].
E.P. Verlinde and H.L. Verlinde, Multiloop calculations in covariant superstring theory, Phys. Lett. B 192 (1987) 95 [INSPIRE].
E. D’Hoker and D.H. Phong, The geometry of string perturbation theory, Rev. Mod. Phys. 60 (1988) 917 [INSPIRE].
R. Saroja and A. Sen, Picture changing operators in closed fermionic string field theory, Phys. Lett. B 286 (1992) 256 [hep-th/9202087] [INSPIRE].
A. Belopolsky, Picture changing operators in supergeometry and superstring theory, hep-th/9706033 [INSPIRE].
E. Witten, Superstring perturbation theory revisited, arXiv:1209.5461 [INSPIRE].
B. Jurčo and K. Muenster, Type II superstring field theory: geometric approach and operadic description, JHEP 04 (2013) 126 [arXiv:1303.2323] [INSPIRE].
A. Sen, Gauge invariant 1PI effective action for superstring field theory, JHEP 06 (2015) 022 [arXiv:1411.7478] [INSPIRE].
A. Sen, Gauge invariant 1PI effective superstring field theory: inclusion of the Ramond sector, JHEP 08 (2015) 025 [arXiv:1501.00988] [INSPIRE].
I.A. Batalin and G.A. Vilkovisky, Gauge algebra and quantization, Phys. Lett. B 102 (1981) 27 [INSPIRE].
I.A. Batalin and G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators, Phys. Rev. D 28 (1983) 2567 [Erratum ibid. D 30 (1984) 508] [INSPIRE].
A.S. Schwarz, Geometry of Batalin-Vilkovisky quantization, Commun. Math. Phys. 155 (1993) 249 [hep-th/9205088] [INSPIRE].
N. Berkovits, Constrained BV description of string field theory, JHEP 03 (2012) 012 [arXiv:1201.1769] [INSPIRE].
B. Zwiebach, Closed string field theory: quantum action and the BV master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [INSPIRE].
M.R. Gaberdiel and B. Zwiebach, Tensor constructions of open string theories. 1: foundations, Nucl. Phys. B 505 (1997) 569 [hep-th/9705038] [INSPIRE].
K. Goto and H. Kunitomo, Construction of action for heterotic string field theory including the Ramond sector, arXiv:1606.07194 [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].
C.R. Preitschopf, C.B. Thorn and S.A. Yost, Superstring field theory, Nucl. Phys. B 337 (1990) 363 [INSPIRE].
I. Ya. Arefeva, P.B. Medvedev and A.P. Zubarev, New representation for string field solves the consistency problem for open superstring field theory, Nucl. Phys. B 341 (1990) 464 [INSPIRE].
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Matsunaga, H. Comments on complete actions for open superstring field theory. J. High Energ. Phys. 2016, 115 (2016). https://doi.org/10.1007/JHEP11(2016)115
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DOI: https://doi.org/10.1007/JHEP11(2016)115