Journal of High Energy Physics

, Volume 2015, Issue 12, pp 1–55 | Cite as

Modular operads and the quantum open-closed homotopy algebra

  • Martin Doubek
  • Branislav Jurčo
  • Korbinian Münster
Open Access
Regular Article - Theoretical Physics

Abstract

We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are explained from the operadic point of view.

Keywords

Non-Commutative Geometry String Field Theory 

References

  1. [1]
    S. Barannikov, Modular operads and Batalin-Vilkovisky geometry, Int. Math. Res. Not. (2007) rnm075.Google Scholar
  2. [2]
    J. Chuang and A. Lazarev, Feynman diagrams and minimal models for operadic algebras, J. London Math. Soc. 81 (2010) 317 [arXiv:0802.3507].MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    M. Doubek, The modular envelope of the cyclic operad Ass, arXiv:1312.5501.
  4. [4]
    E. Getzler and M.M. Kapranov, Modular operads, Composit. Math. 110 (1998) 65 [dg-ga/9408003].
  5. [5]
    E. Getzler and M.M. Kapranov, Cyclic operads and cyclic homology, in Geometry, topology & physics, Conf. Proc. Lecture Notes Geom. Topology IV, Int. Press, Cambridge MA U.S.A. (1995), pg. 167.Google Scholar
  6. [6]
    M. Herbst, Quantum A-infinity structures for open-closed topological strings, hep-th/0602018 [INSPIRE].
  7. [7]
    H. Kajiura and J. Stasheff, Homotopy algebras inspired by classical open-closed string field theory, Commun. Math. Phys. 263 (2006) 553 [math/0410291] [INSPIRE].
  8. [8]
    H. Kajiura and J. Stasheff, Open-closed homotopy algebra in mathematical physics, J. Math. Phys. 47 (2006) 023506 [hep-th/0510118] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    R.M. Kaufmann, B.C. Ward and J.J. Zuniga, The odd origin of Gerstenhaber, BV and the master equation, arXiv:1208.5543 [INSPIRE].
  10. [10]
    J.-L. Loday and B. Vallette, Algebraic operads, Springer, Heidelberg Germany (2012) [ISBN:978-3-642-30361-6].Google Scholar
  11. [11]
    A. Luk’acs, Cyclic operads, Dendoridal structure, higher categories, thesis, (2010).Google Scholar
  12. [12]
    M. Markl, S. Shnider and S. Stasheff, Operads in algebra, topology and physics, Mathematical Surveys and Monographs 96, AMS, U.S.A. (2002).Google Scholar
  13. [13]
    M. Markl, Loop homotopy algebras in closed string field theory, Commun. Math. Phys. 221 (2001) 367 [hep-th/9711045] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    K. Munster and I. Sachs, Quantum open-closed homotopy algebra and string field theory, Commun. Math. Phys. 321 (2013) 769 [arXiv:1109.4101] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    K. Münster and I. Sachs, Homotopy classification of bosonic string field theory, Commun. Math. Phys. 330 (2014) 1227 [arXiv:1208.5626] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    B. Zwiebach, Closed string field theory: quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    B. Zwiebach, Oriented open-closed string theory revisited, Annals Phys. 267 (1998) 193 [hep-th/9705241] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Martin Doubek
    • 1
  • Branislav Jurčo
    • 1
  • Korbinian Münster
    • 2
  1. 1.Charles University, Faculty of Mathematics and PhysicsPragueCzech Republic
  2. 2.Arnold Sommerfeld Center for Theoretical PhysicsMunichGermany

Personalised recommendations