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We propose a geometric characterisation of the topological string partition functions associated to the local Calabi-Yau (CY) manifolds used in the geometric engineering of $d=4$, $\mathcal{N}=2$ supersymmetric field theories of class…
It is an important question in string compactification whether complex structure moduli stabilization inevitably ends up with a vacuum expectation value of the superpotential < W > of the order of the Planck scale cubed. Any thoughts on…
In this paper we consider heterotic compactifications on K3 x T2 as well as type II compactifications on K3-fibred Calabi-Yau spaces with certain fluxes for the gauge and RR field strengths F and H turned on. By providing an identification…
This thesis is concerned with heterotic E8 x E8 string models that can produce quasirealistic N = 1 supersymmetric extensions of the Standard Model in the low-energy limit. We start rather generally by deriving the four-dimensional spectrum…
These are notes based on lectures given at TASI99. We review the geometry of the moduli space of N=2 theories in four dimensions from the point of view of superstring compactification. The cases of a type IIA or type IIB string compactified…
It is shown that the entropy of fourdimensional black holes in string theory compactified on weighted Calabi-Yau hypersurfaces shows scaling behavior in a certain limit. This leads to non-monotonic functions on the moduli space.
The Kahler potential is the least understood part of effective N=1 supersymmetric theories derived from string compactifications. Even at tree-level, the Kahler potential for the physical matter fields, as a function of the moduli fields,…
We study the topological conditions for general Calabi-Yaus to get a non-supersymmetric AdS exponentially large volume minimum of the scalar potential in flux compactifications of IIB string theory. We show that negative Euler number and…
In this work, we study the local zeta functions of Calabi-Yau fourfolds. This is done by developing arithmetic deformation techniques to compute the factor of the zeta function that is attributed to the horizontal four-form cohomology.…
The N=1 effective action for generic type IIA Calabi-Yau orientifolds in the presence of background fluxes is computed from a Kaluza-Klein reduction. The Kahler potential, the gauge kinetic functions and the flux-induced superpotential are…
In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten…
String theory is the prime candidate for the theory of everything. However, it must be defined in ten dimensions to be consistent. To get 4D physics, the 6 other dimensions should be curled up in a small compact manifold, this procedure is…
The self-dual Einstein equations on a compact Riemannian 4-manifold can be expressed as a quadratic condition on the curvature of an $SU(2)$ (spin) connection which is a covariant generalization of the self-dual Yang-Mills equations. Local…
We propose, based on the viewpoint that our three-dimensional space is a stack of BPS D3-branes located at the conifold singularity of the Calabi-Yau three-fold, a new mechanism to address the cosmological constant problem in the framework…
The heterotic $SU(3)$ system, also known as the Hull--Strominger system, arises from compactifications of heterotic string theory to six dimensions. This paper investigates the local structure of the moduli space of solutions to this system…
We discuss a number of issues arising when computing non-perturbative effects systematically across the string theory landscape. In particular, we cast the study of fairly generic physical properties into the language of…
Some selected applications of KT and HKT geometries in string theory, supergravity, black hole moduli spaces and hermitian geometry are reviewed. It is shown that the moduli spaces of a large class of five-dimensional supersymmetric black…
This paper studies the Chow and cohomology rings of the Hacking moduli stack $\mathcal{P}^{\mathrm{H}}$ of plane quartics. We construct a smooth proper Deligne--Mumford stack resolving the Calabi--Yau wall crossing between the KSBA and…
We review cosmological solutions of type II superstrings and M-theory, emphasizing the role of non-vanishing Ramond form backgrounds. Compactifications on flat and, more generally, maximally symmetric spatial subspaces are presented. We…
Heterotic string compactifications on integrable $G_2$ structure manifolds $Y$ with instanton bundles $(V,A), (TY,\tilde{\theta})$ yield supersymmetric three-dimensional vacua that are of interest in physics. In this paper, we define a…