Related papers: Homotopy algebras inspired by classical open-close…

Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a…

We explain how the spacetime diffeomorphism in the classical bosonic closed string field theory (SFT) is represented as $L_\infty$ gauge transformations in weakly curved backgrounds. In particular, we demonstrate the explicit map between…

We verify that certain algebras appearing in string field theory are algebras over Feynman transform of modular operads which we describe explicitly. Equivalent description in terms of solutions of generalized BV master equations are…

We use the new nilpotent formulation of open-closed string field theory to explore the limit where the number $N$ of identical D-branes of the starting background is large. By reformulating the theory in terms of the 't Hooft coupling…

String backgrounds are described as purely geometric objects related to moduli spaces of Riemann surfaces, in the spirit of Segal's definition of a conformal field theory. Relations with conformal field theory, topological field theory and…

We develop a general framework for the construction of various derived brackets. We show that suitably deforming the differential of a graded Leibniz algebra extends the derived bracket construction and leads to the notion of strong…

We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.

Two cochain complexes are constructed for an algebra A and a coalgebra C entwined with each other via the map $\psi:C\otimes A\to A\otimes C$. One complex is associated to an A-bimodule, the other to a C-bicomodule. In the former case the…

We determine the \emph{$L_\infty$-algebra} that controls deformations of a relative Rota-Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling deformations of the underlying LieRep pair by the dg Lie algebra…

Let G be a compact Lie group. By work of Chataur and Menichi, the homology of the space of free loops in the classifying space of G is known to be the value on the circle in a homological conformal field theory. This means in particular…

Homotopy algebraic methods have become increasingly influential in studying field theories. We consider semi-holomorphic Chern-Simons theory and its relation with the principal chiral model. In particular, we establish an explicit…

We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…

In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…

We investigate analytic classical solutions in open string field theory which are constructed in terms of marginal operators. In the classical background, we evaluate a coupling between an on-shell closed string state and the open string…

We prove a filtered version of the Homotopy Transfer Theorem which gives an A-infinity algebra structure on any page of the spectral sequence associated to a filtered dg-algebra. We then develop various applications to the study of the…

Koschorke introduced a map from the space of closed $n$-component links to the ordered configuration space of $n$-tuples of points in $\mathbb{R}^3$, and conjectured that this map separates homotopy links. The purpose of this paper is to…

This is the second paper of a series of three. We construct effective open-closed superstring couplings by classically integrating out massive fields from open superstring field theories coupled to an elementary gauge invariant tadpole…

We investigate the Hopf algebra structure in string worldsheet theory and give a unified formulation of the quantization of string and the space-time symmetry. We reformulate the path integral quantization of string as a Drinfeld twist at…

In paper arXiv:1406.1744, we constructed a symmetric monoidal category $LIE^{MC}$ whose objects are shifted (and filtered) L-infinity algebras. Here, we fix a cooperad $C$ and show that algebras over the operad $Cobar(C)$ naturally form a…

Motivated by string field theory, we explore various algebraic aspects of higher spin theory and Vasiliev equation in terms of homotopy algebras. We present a systematic study of unfolded formulation developed for the higher spin equation…