Related papers: Closed string operators in topology leading to Lie…
To open-closed cobordism surfaces, open-closed string topology associates topological quantum field theory (TQFT) operations, namely string operations, which depend only on homeomorphism types of surfaces and which satisfy the sewing…
In this expository paper we discuss a project regarding the string topology of a manifold, that was inspired by recent work of Moore-Segal, Costello, and Hopkins and Lurie, on "open-closed topological conformal field theories". Given a…
Quantum Lefschetz theorem by Coates and Givental gives a relationship between the genus 0 Gromov-Witten theory of X and the twisted theory by a line bundle L on X. We prove the convergence of the twisted theory under the assumption that the…
We argue that all conjectured dualities involving various string, M- and F- theory compactifications can be `derived' from the conjectured duality between type I and SO(32) heterotic string theory, T-dualities, and the definition of M- and…
For the simple Lie algebra $ \frak{so}_m$, we study the commutant vertex operator algebra of $ L_{\hat{\frak{so}}_{m}}(n,0)$ in the $n$-fold tensor product $ L_{\hat{\frak{so}}_{m}}(1,0)^{\otimes n}$. It turns out that this commutant vertex…
We define the notions of unital/counital/biunital infinitesimal anti-symmetric bialgebras and coFrobenius bialgebras and discuss their algebraic properties. We also define the notion of a graded 2D open-closed TQFT. These structures arise…
The structure of spacetime duality and discrete worldsheet symmetries of compactified string theory is examined within the framework of noncommutative geometry. The full noncommutative string spacetime is constructed using the…
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 lay out an approach to derive the closed string dual to the simplest possible gauge theory, a single hermitian matrix integral, in the conventional 't Hooft large $N$ limit. In this first installment of three papers, we propose and…
We display a family of Stone-type dualities linking categories of frames carrying pairs of modal operators to categories of spaces carrying a binary relation. Different notions of morphism used on the relational side lead to significant…
The paper discusses the connection between S-duality and string-theoretic picture-changing formalism. The singular limit of the picture-changing transformation at zero momentum leads to the presence of the topological 5-form charge in the…
This review provides an introduction to non-geometric backgrounds in string theory. Starting from a discussion of T-duality, geometric and non-geometric torus-fibrations are reviewed, generalised geometry and its relation to non-geometric…
Let M be a closed, oriented, n-dimensional manifold. In this paper we give a Morse theoretic description of the string topology operations introduced by Chas and Sullivan, and extended by the first author, Jones, Godin, and others. We do…
We propose a general method to study open/closed string dualities from transitions in M theory which is valid for a large class of geometrical configurations. By T-duality we can transform geometrically engineered configurations into N = 1…
Orbifold and logarithmic structures provide independent routes to the virtual enumeration of curves with tangency orders for a simple normal crossings pair $(X|D)$. The theories do not coincide and their relationship has remained…
We study stable maps to normal crossings pairs with possibly negative tangency orders. There are two independent models: punctured Gromov-Witten theory of pairs and orbifold Gromov-Witten theory of root stacks with extremal ages. Exploiting…
The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate…
We study topological open membranes of BF type in a manifest BV formalism. Our main interest is the effect of the bulk deformations on the algebra of boundary operators. This forms a homotopy Lie algebra, which can be understood in terms of…
Tests of the integrality properties of a scalar operator in topological strings on a resolved conifold background or orientifold of conifold backgrounds have been performed for arborescent knots and some non-arborescent knots. The recent…
The string theory on symmetric product describes the second-quantized string theory. The development for the bosonic open string was discussed in the previous work. In this paper, we consider the open superstring theory on the symmetric…