Type II superstring field theory: geometric approach and operadic description
Open Access
ArticleFirst Online:
- 270 Downloads
- 3 Citations
Abstract
We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach’s construction for the bosonic string. The construction uses the small Hilbert space. Elementary vertices of the non-polynomial action are described with the help of a properly formulated minimal area problem. They give rise to an infinite tower of superstring field products defining a \( \mathcal{N} \) = 1 generalization of a loop homotopy Lie algebra, the genus zero part generalizing a homotopy Lie algebra. Finally, we give an operadic interpretation of the construction.
Keywords
Superstrings and Heterotic Strings String Field Theory Download
to read the full article text
References
- [1]E. Witten, Interacting field theory of open superstrings, Nucl. Phys. B 276 (1986) 291 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
- [2]E. Witten, Noncommutative geometry and string field theory, Nucl. Phys. B 268 (1986) 253 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
- [3]C. Wendt, Scattering amplitudes and contact interactions in Witten’s superstring field theory, Nucl. Phys. B 314 (1989) 209 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
- [4]C.R. Preitschopf, C.B. Thorn and S.A. Yost, Superstring field theory, Nucl. Phys. B 337 (1990) 363 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
- [5]I.Y. Arefeva, P. Medvedev and A. Zubarev, New representation for string field solves the consistency problem for open superstring field theory, Nucl. Phys. B 341 (1990) 464 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
- [6]M. Kroyter, Superstring field theory equivalence: Ramond sector, JHEP 10 (2009) 044 [arXiv:0905.1168] [INSPIRE].ADSGoogle Scholar
- [7]N. Berkovits, SuperPoincaré invariant superstring field theory, Nucl. Phys. B 450 (1995) 90 [Erratum ibid. B 459 (1996) 439] [hep-th/9503099] [INSPIRE].
- [8]N. Berkovits, Constrained BV description of string field theory, JHEP 03 (2012) 012 [arXiv:1201.1769] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
- [9]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].MathSciNetADSCrossRefGoogle Scholar
- [10]M. Kroyter, Superstring field theory in the democratic picture, Adv. Theor. Math. Phys. 15 (2011) 741 [arXiv:0911.2962] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
- [11]B. Zwiebach, Closed string field theory: quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
- [12]C.J. Yeh, Topics in superstring theory, Dissertation Abstracts International, 55–07, section B, (1993) [INSPIRE].
- [13]A. Belopolsky, New geometrical approach to superstrings, hep-th/9703183 [INSPIRE].
- [14]L. Álvarez-Gaumé, C. Gomez, P.C. Nelson, G. Sierra and C. Vafa, Fermionic strings in the operator formalism, Nucl. Phys. B 311 (1988) 333 [INSPIRE].ADSCrossRefGoogle Scholar
- [15]T. Voronov, Geometric integration theory on supermanifolds, Soviet Scientific Reviews: section C - Mathematical Physics Reviews, Harwood Academic, (1991).Google Scholar
- [16]A. Belopolsky, Picture changing operators in supergeometry and superstring theory, hep-th/9706033 [INSPIRE].
- [17]S. Barannikov, Modular operads and Batalin-Vilkovisky geometry, Int. Math. Res. Notices (2007) rnm075.Google Scholar
- [18]M. Markl, Loop homotopy algebras in closed string field theory, Commun. Math. Phys. 221 (2001) 367 [hep-th/9711045] [INSPIRE].MathSciNetADSCrossRefzbMATHGoogle Scholar
- [19]E. Witten, Notes on supermanifolds and integration, arXiv:1209.2199 [INSPIRE].
- [20]E. Witten, Notes on super Riemann surfaces and their moduli, arXiv:1209.2459 [INSPIRE].
- [21]A. Sen and B. Zwiebach, Quantum background independence of closed string field theory, Nucl. Phys. B 423 (1994) 580 [hep-th/9311009] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
- [22]E. Getzler, Batalin-Vilkovisky algebras and two-dimensional topological field theories, Commun. Math. Phys. 159 (1994) 265 [hep-th/9212043] [INSPIRE].MathSciNetADSCrossRefzbMATHGoogle Scholar
- [23]E. Witten, Superstring perturbation theory revisited, arXiv:1209.5461 [INSPIRE].
- [24]B. DeWitt, Supermanifolds, Cambridge Monographs on Mathematical Physics, Cambridge U.K. (1992).Google Scholar
- [25]E. Getzler and M.M. Kapranov, Modular operads, Compositio Math. 110 (1998) 65 [dg-ga/9408003].MathSciNetCrossRefzbMATHGoogle Scholar
- [26]M. Markl, S. Shnider and J.D. Stasheff, Operads in algebra, topology and physics, AMS Mathematical Surveys and Monographs 96, Providence U.S.A. (2002).Google Scholar
- [27]V. Ginzburg and M. Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994) 203 [arXiv:0709.1228].MathSciNetCrossRefGoogle Scholar
- [28]Y. Okawa and B. Zwiebach, Heterotic string field theory, JHEP 07 (2004) 042 [hep-th/0406212] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
- [29]R. Donagi and E. Witten, to appear.Google Scholar
- [30]K. Muenster and I. Sachs, Homotopy classification of bosonic string field theory, arXiv:1208.5626 [INSPIRE].
- [31]K. Costello, Topological conformal field theories and Calabi-Yau categories, Adv. Math. 210 (2007) 165 [math.QA/0412149] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
- [32]M. Doubek, B. Jurco and K. Muenster, Modular operads and the quantum open-closed homotopy algebra, in preparation.Google Scholar
- [33]K. Muenster and I. Sachs, Quantum open-closed homotopy algebra and string field theory, arXiv:1109.4101 [INSPIRE].
- [34]D. Friedan, E.J. Martinec and S.H. Shenker, Conformal invariance, supersymmetry and string theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].MathSciNetADSGoogle Scholar
- [35]J.J. Atick and A. Sen, Spin field correlators on an arbitrary genus Riemann surface and nonrenormalization theorems in string theories, Phys. Lett. B 186 (1987) 339 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
Copyright information
© SISSA 2013