This paclet contains computable aspects of a version of Chern-Simons theory announced by Cieliebak, Fukaya and Latschev, defined by Cieliebak and Volkov and, among others, studied in Hájek's PhD thesis. It corresponds to the large-n limit of U(n) Chern-Simons theory on a closed oriented manifold (see also the recent paper of Hamilton).

It can be formulated on the cyclic words of the de Rham cohomology either as an IBL-infinity Maurer-Cartan element of a canonical involutive bi-Lie algebra (IBL), or equivalently, as a Beilinson-Drinfeld action of a canonical BD operator. The action defines an open string field theory on the de Rham cohomology that corresponds to a quantum A-infinity algebra generalizing Stasheff's A-infinity homotopy transfer from trees to trivalent ribbon graphs (see Münster and Sachs).

This open string field theory can be thought of as the open sector of an open-closed string field theory (Münster and Sachs), with the closed part being the symplectic field theory of the unit cotangent bundle, and the IBL-infinity morphism between the canonical IBL algebra twisted by the Maurer-Cartan element and the IBL-infinity algebra of symplectic field theory twisted by the canonical augmentation being obtained by integrating forms over the moduli spaces of holomorphic curves with boundary punctures on the zero section (open string insertions), where the forms are pulled back, and interior punctures asymptotic to Reeb orbits (closed string insertions).

If the manifold is simply connected, the structure is related to string topology: the twisted IBL-infinity algebra is a chain model of Chas-Sullivan equivariant string topology relative to a base point, via Chen's iterated integrals. If the manifold is homologically simply connected, strong vanishing results hold (Cieliebak, Hájek and Volkov) and the structure can be equivalently computed by taking a Poincaré duality model of the de Rham cohomology and the canonical IBL algebra on its cyclic words equipped with the cyclic Hochschild differential.

The areas of the paclet are the canonical Lie bialgebras of cyclic words, the Beilinson-Drinfeld formalism with its Maurer-Cartan elements, the algebraic models from which the graded alphabet of the cyclic words is read, and the homotopy algebras. Each area has its own guide.