Further Reading
53
Recently, an alternative decomposition of the closed string moduli space in terms of
hyperbolic string vertices has been proposed in
• K. Costello and B. Zwiebach, “Hyperbolic string vertices”, arXiv:1909.00033.
The first proof of local background invariance of closed string field theory
appeared in
• A. Sen and B. Zwiebach, “A proof of local background independence of classical
closed string field theory”, Phys. B414 (1994) 649–714.
Our description on this topic follows
• K. Munster and I. Sachs, “Homotopy classification of bosonic string field
theory”, Commun. Math. Phys. 330 (2014) 1227–1262.
In our description of the measure on the moduli space we followed Witten’s notes
• E. Witten, “Perturbative superstring theory”, arXiv:1209.5461.
For a modern review of closed superstring field theory, see, e.g.
• C. de Lacroix H. Erbin, S. P. Kashyap, A. Sen, M. Vermaet, “Closed superstring
field theory and its applications”, Int. J. Mod. Phys. A32, (2017), and
• T. Erler, “Four lectures on closed string field theory”, arXiv:1905.06785.
A derivation of the L ∞ -structure of closed string field theory can be found in
• H. Kajiura and J. Stasheff, “Homotopy algebras inspired by classical open-closed
string field theory”, Commun. Math. Phys. 263, 553–581 (2006).
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.
One description of the appropriate complex on the moduli space of (bordered)
Riemann surfaces with punctures can be found in
• E. Harrelson, A.A. Voronov and J. J. Zuniga, “Open-closed moduli spaces and
related algebraic structures”, Lett. Math. Phys. 94 (2010), no. 1, 1–26.
53
Recently, an alternative decomposition of the closed string moduli space in terms of
hyperbolic string vertices has been proposed in
• K. Costello and B. Zwiebach, “Hyperbolic string vertices”, arXiv:1909.00033.
The first proof of local background invariance of closed string field theory
appeared in
• A. Sen and B. Zwiebach, “A proof of local background independence of classical
closed string field theory”, Phys. B414 (1994) 649–714.
Our description on this topic follows
• K. Munster and I. Sachs, “Homotopy classification of bosonic string field
theory”, Commun. Math. Phys. 330 (2014) 1227–1262.
In our description of the measure on the moduli space we followed Witten’s notes
• E. Witten, “Perturbative superstring theory”, arXiv:1209.5461.
For a modern review of closed superstring field theory, see, e.g.
• C. de Lacroix H. Erbin, S. P. Kashyap, A. Sen, M. Vermaet, “Closed superstring
field theory and its applications”, Int. J. Mod. Phys. A32, (2017), and
• T. Erler, “Four lectures on closed string field theory”, arXiv:1905.06785.
A derivation of the L ∞ -structure of closed string field theory can be found in
• H. Kajiura and J. Stasheff, “Homotopy algebras inspired by classical open-closed
string field theory”, Commun. Math. Phys. 263, 553–581 (2006).
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.
One description of the appropriate complex on the moduli space of (bordered)
Riemann surfaces with punctures can be found in
• E. Harrelson, A.A. Voronov and J. J. Zuniga, “Open-closed moduli spaces and
related algebraic structures”, Lett. Math. Phys. 94 (2010), no. 1, 1–26.