Related papers: The Atiyah Class and Complex Structure Stabilizati…
We investigate the relationship between supersymmetric gauge theories with moduli spaces and matrix models. Particular attention is given to situations where the moduli space gets quantum corrected. These corrections are controlled by…
In this work we review a systematic, algorithmic construction of dual heterotic/F-theory geometries corresponding to 4-dimensional, N = 1 supersymmetric compactifications. We look in detail at a class of well-defined Calabi-Yau fourfolds…
We discuss the vacuum structure of type IIA/B Calabi-Yau string compactifications to four dimensions in the presence of n-form H-fluxes. These will lift the vacuum degeneracy in the Calabi-Yau moduli space, and for generic points in the…
The moduli space of generalized deformations of a Calabi-Yau hypersurface is computed in terms of the Jacobian ring of the defining polynomial. The fibers of the tangent bundle to this moduli space carry algebra structures, which are…
Achieving full moduli stabilisation in type IIB string compactifications for generic Calabi-Yau threefolds with hundreds of K\"ahler moduli is notoriously hard. This is due not just to the very fast increase of the computational complexity…
We consider four dimensional heterotic compactifications on smooth elliptic Calabi-Yau threefolds. Using spectral cover techniques, we study bundle cohomology groups corresponding to charged matter multiplets. The analysis shows that in…
We study periods in an integral basis near all possible singularities in one-dimensional complex structure moduli spaces of Calabi-Yau threefolds. Near large complex structure points these asymptotic periods are well understood in terms of…
We discuss some aspects of perturbative $(0,2)$ Calabi-Yau moduli space. In particular, we show how models with different $(0,2)$ data can meet along various sub-loci in their moduli space. In the simplest examples, the models differ by the…
We show that six-dimensional backgrounds that are T^2 bundle over a Calabi-Yau two-fold base are consistent smooth solutions of heterotic flux compactifications. We emphasize the importance of the anomaly cancellation condition which can…
We study topology change in M theory compactifications on Calabi-Yau three-folds in the presence of G flux (the four form field strength). In particular, we discuss vacuum solutions in strongly coupled heterotic string theory in which the…
In this paper we discuss compactifications of type II superstrings where the moduli of the internal Calabi-Yau space vary over four-dimensional space time. The corresponding solutions of four-dimensional N=2 supergravity are given by…
We shall obtain unobstructed deformations of four geometric structures: Calabi-Yau, HyperK\"ahler, $\G$ and Spin(7) structures in terms of closed differential forms (calibrations). We develop a direct and unified construction of smooth…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
Given a compact hyperkaehler manifold $M$ and a holomorphic bundle B over $M$, we consider a Hermitian connection $\nabla$ on B which is compatible with all complex structures on $M$ induced by the hyperkaehler structure. Such a connection…
We introduce the notion of Atiyah class of a generalized holomorphic vector bundle, which captures the obstruction to the existence of generalized holomorphic connections on the bundle. As in the classical holomorphic case, this Atiyah…
Heterotic orbifold compactifications yield a myriad of models that reproduce many properties of the supersymmetric extension of the standard model and provide potential solutions to persisting problems of high energy physics, such as the…
We examine the mechanism of moduli stabilization by fluxes in the limit of a large number of moduli. We conjecture that one cannot stabilize all complex-structure moduli in F-theory at a generic point in moduli space (away from…
We study moduli stabilization by thermal effects in the cosmological context. The implementation of finite temperature, which spontaneously breaks supersymmetry, induces an effective potential at one loop level. At the points where extra…
Cohesive modules give a dg-enhancement of the bounded derived category of coherent sheaves on a complex manifold via superconnections. In this paper we discuss the deformation theory of cohesive modules on compact complex manifolds. This…
Several situations are known when a holomorphic 2-form on a moduli space of sheaves over some base S is induced by a holomorphic 2-form on S. Moreover, the closedness of the 2-form on the base implies the closedness on the moduli space,…