Open-closed modular operads, the Cardy condition and string field theory

0499147 - MÚ 2019 RIV CH eng J - Journal Article
Doubek, M. - Markl, Martin
Open-closed modular operads, the Cardy condition and string field theory.
Journal of Noncommutative Geometry. Roč. 12, č. 4 (2018), s. 1359-1424. ISSN 1661-6952. E-ISSN 1661-6960
Institutional support: RVO:67985840
Keywords : modular completion * Frobenius algebra * open and closed strings
OECD category: Pure mathematics
Impact factor: 0.826, year: 2018
http://www.ems-ph.org/journals/show_abstract.php?issn=1661-6952&vol=12&iss=4&rank=5

We prove that the modular operad of diffeomorphism classes of Riemann surfaces with both “open” and “closed” boundary components, in the sense of string field theory, is the modular completion of its genus 0 part quotiented by the Cardy condition. We also provide a finitary presentation of a version of this modular two-colored operad and characterize its algebras via morphisms of Frobenius algebras, recovering some previously known results of Kaufmann, Penner and others. As an important auxiliary tool we characterize inclusions of cyclic operads that induce inclusions of their modular completions.
Permanent Link: http://hdl.handle.net/11104/0291414