Related papers: Background Independent Algebraic Structures in Clo…
For logarithmic conformal field theories whose monodromy data is given by a not necessarily semisimple modular category, we solve the problem of constructing and classifying the consistent systems of correlators. The correlator construction…
We argue that the Leutheusser-Liu procedure of isolating a von Neumann algebra in the $N = \infty$ limit of string theories, leads to the algebra of relativistic fermion fields on a half line for the $c = 1$ string theory. This is a Type…
We first review various known algebraic structures on the Hochschild (co)homology of a differential graded algebras under weak Poincar{\'e} duality hypothesis, such as Calabi-Yau algebras, derived Poincar{\'e} duality algebras and closed…
Motivated by the descent equation in string theory, we give a new interpretation for the action of the symmetry charges on the BRST cohomology in terms of what we call {\em the Gerstenhaber bracket}. This bracket is compatible with the…
Toda Conformal Field Theories (CFTs hereafter) are generalizations of Liouville CFT where the underlying field is no longer scalar but takes values in a finite-dimensional vector space induced by a complex simple Lie algebra. The goal of…
We give a criterion for the complete reducibility of modules satisfying a composability condition for a meromorphic open-string vertex algebra $V$ using the first cohomology of the algebra. For a $V$-bimodule $M$, let…
Multi-brane backgrounds are studied in the framework of the background independent open string field theory. A simple description of the non-abelian degrees of freedom is given. Algebra of the differential operators acting on the space of…
A two-dimensional topological sigma-model on a generalized Calabi-Yau target space $X$ is defined. The model is constructed in Batalin-Vilkovisky formalism using only a generalized complex structure $J$ and a pure spinor $\rho$ on $X$. In…
We introduce a family of maps parametrised by certain ribbon graphs. It is based on a connection in non-commutative geometry and contains the double divergence as a special case. Applying the construction to the case of the group algebra of…
The purpose of this paper is to explain and to generalize, in a homotopical way, the result of Barannikov-Kontsevich and Manin which states that the underlying homology groups of some Batalin-Vilkovisky algebras carry a Frobenius manifold…
Given a differential graded (dg) symmetric Frobenius algebra $A$ we construct an unbounded complex $\mathcal{D}^{*}(A,A)$, called the Tate-Hochschild complex, which arises as a totalization of a double complex having Hochschild chains as…
A framework for background independent open-string field theory is proposed. The approach involves using the BV formalism -- in a way suggested by recent developments in closed-string field theory -- to implicitly define a gauge invariant…
We solve the problem of constructing a genus-zero full conformal field theory (a conformal field theory on genus-zero Riemann surfaces containing both chiral and antichiral parts) from representations of a simple vertex operator algebra…
We study linear Batalin-Vilkovisky (BV) quantization, which is a derived and shifted version of the Weyl quantization of symplectic vector spaces. Using a variety of homotopical machinery, we implement this construction as a symmetric…
We study Witten's open string field theory in the presence of a constant B field. We construct the string field theory in the operator formalism and find that, compared to the ordinary theory with no B field, the vertices in the resulting…
We define a structure of an algebra on the Lagrangian Floer cohomology of a Lagrangian submanifold over the quantum cohomology of the ambient symplectic manifold. The structure is analogous to the one defined by Biran-Cornea, but is…
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. It was previously shown by the author that the Hochschild cohomology of a hom-associative algebra $A$ carries a Gerstenhaber structure. In…
We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach's construction for the bosonic string. The construction uses the small Hilbert space. Elementary…
Let $\Delta$ be a finite set of nonzero linear forms in several variables with coefficients in a field $\mathbf K$ of characteristic zero. Consider the $\mathbf K$-algebra $C(\Delta)$ of rational functions generated by $\{1/\alpha \mid…
The construction of superintegrable systems based on Lie algebras and their universal enveloping algebras has been widely studied over the past decades. However, most constructions rely on explicit differential operator realisations and…