Further Reading
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Further Reading
For a detailed derivation of the open-closed BV bracket and the corresponding BV
action see
• B. Zwiebach, “Oriented open-closed string theory revisited”, Annals Phys. 267,
(1998) 193.
The classical open-closed homotopy algebra was derived in
• H. Kajiura, J. Stasheff, “Open-closed homotopy algebra in mathematical
physics”, J. Math. Phys. 47, 023506 (2006).
Our description of the quantum open-closed homotopy algebra in this chapter is
based on
• K. Münster and I. Sachs, “Quantum Open-Closed Homotopy Algebra and String
Field Theory”, Commun. Math. Phys. 321 (2013) 769.
For a detailed description of the IBL ∞ algebra underlying quantum closed string
theory see
• K. Cieliebak, K. Fukaya and J. Latschev, “Homological algebra related to
surfaces with boundary”, arXiv:1508.02741.
A detailed description of the open-closed modular operad can be found in
• M. Doubek and M. Markl, “Open-closed modular operads, the Cardy condition
and string field theory”, J. Noncommut. Geom. 12(4)(2018), 1359–1424.
The quantum open-closed homotopy algebra and its operadic origin are discussed in
• M. Doubek, B. Jurˇ co and K. Münster, “Modular operads and the quantum openclosed homotopy algebra”, JHEP 2015(12), 1–55.