Related papers: Cohomological vertex operators
We construct complete sets of (open and closed string) covariant coherent state and mass eigenstate vertex operators in bosonic string theory. By minimally extending the standard definition of coherent states so as to include the string…
The moduli stack of representations of a quiver, or coherent sheaves on a proper curve, carries two structures on its cohomology: a Hall algebra and braided vertex coalgebra. We show that they are compatible, by developing a formulation of…
We construct more dual pairs of type II-heterotic strings in four dimensions with $N=2,1$ spacetime supersymmetry. On the type II side the construction utilizes the various possible choices of K3 automorphisms with fixed points which…
We study the quantum volume of D-branes wrapped around various cycles in Calabi-Yau manifolds, as the manifold's moduli are varied. In particular, we focus on the behaviour of these D-branes near phase transitions between distinct low…
Recently, a correspondence has been proposed between spectral theory and topological strings on toric Calabi-Yau manifolds. In this paper we develop in detail this correspondence for mirror curves of higher genus, which display many new…
We study four-dimensional black hole configurations which result from wrapping M5-branes on a Calabi-Yau manifold, as well as U-dual realizations. Our aim is to understand the microscopic degrees of freedom responsible for the existence of…
We briefly review attempts to construct string theories that yield the standard model, concentrating on models with a geometric interpretation. Calabi-Yau compactifications are discussed in the context of both the weakly coupled heterotic…
The space of differential operators acting on skewsymmetric tensor fields or on smooth forms of a smooth manifold are representations of its Lie algebra of vector fields. We compute the first cohomology spaces of these representations and…
This review is devoted to strings and branes. Firstly, perturbative string theory is introduced. The appearance of various types of branes is discussed. These include orbifold fixed planes, D-branes and orientifold planes. The connection to…
In this dissertation, we study various aspects of type IIB string theory compactified on freely acting orbifolds. We focus particularly on asymmetric orbifolds, which are examples of non-geometric string compactifications and constitute an…
We introduce two $K$-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these…
We briefly review the recent programme to construct, systematically and algorithmically, large classes of heterotic vacua, as well as the search for the MSSM therein. Specifically, we outline the monad construction of vector bundles over…
By a direct CFT computation, the spectrum of the topological B-model is compared to Ext groups of sheaves. A match can only be made if abstract vector bundles on holomorphic submanifolds are twisted by the canonical $\mathrm{Spin}^c$…
We study the topological string partition function of a class of toric, double elliptically fibered Calabi-Yau threefolds $X_{N,M}$ at a generic point in the K\"ahler moduli space. These manifolds engineer little string theories in five…
We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $\hat{\mathfrak{g}}$, from $\mathfrak{g}$-module homomorphisms. When…
The second cohomology group of a left skew brace with coefficients in a trivial left brace with non-trivial actions is defined, its connection with extensions of a left skew brace by a trivial braces is established and a Wells' like exact…
Compactifications of heterotic string theory on Generalized Calabi-Yau manifolds have been expected to give the same type of flexibility that type IIB compactifications on Calabi-Yau orientifolds have. In this note we generalize the work…
This work is concerned with branes and differential equations for one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. For a certain class of B-branes we derive the inhomogeneous Picard--Fuchs equations satisfied by the…
Compactifications with fluxes and branes motivate us to study various enumerative invariants of Calabi-Yau manifolds. In this paper, we study non-perturbative corrections depending on both open and closed string moduli for a class of…
We discuss how the geometry of $D2$-$D0$ branes may be related to Gromov-Witten theory of Calabi-Yau threefolds.