Journal of Noncommutative Geometry
Full-Text PDF (629 KB) | Metadata | Table of Contents | JNCG summary
Published online: 2018-12-06
Open-closed modular operads, the Cardy condition and string field theoryMartin Doubek and Martin Markl (1) Czech Academy and Charles University, Prague, Czechia
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.
Keywords: Modular completion, hybrid, open and closed strings, Frobenius algebra
Doubek Martin, Markl Martin: Open-closed modular operads, the Cardy condition and string field theory. J. Noncommut. Geom. 12 (2018), 1359-1424. doi: 10.4171/JNCG/310