Related papers: Small Volumes in Compactified String Theory
The study of the geometry of Calabi-Yau fourfolds is relevant for compactifications of string theory, M-theory, and F-theory to various dimensions. In the first part of this thesis, we study the action of mirror symmetry on two-dimensional…
The main content of this treatise is a new concept in nonperturbative non-Lagrangian QFT which explains and extends the ad hoc constructions in low-dimensional models and incorporates them together with the higher dimensional theories into…
This is a review. Comments are welcome. The observation that the structure of string theory is rich enough to include the standard model in rough outline is an old one, starting with the early constructions of free field constructions,…
We study five-dimensional Kasner cosmologies in a time-dependent Calabi-Yau compactification of M-theory undergoing a flop transition. The dynamics of the additional states, which become massless at the transition point and give rise to a…
We investigate holomorphic anomalies of partition functions underlying string compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic fourfolds the partition functions have an alternative interpretation as elliptic…
In this work we study interesting corners of the quantum gravity landscape with 8 supercharges pushing the boundaries of our current understanding. Calabi-Yau threefolds compactifications of F/M/type II theories to 6, 5 and 4 dimensions are…
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
In the framework of heterotic M-theory compactified on a Calabi-Yau threefold 'times' an interval, the relation between geometry and four-flux is derived {\it beyond first order}. Besides the case with general flux which cannot be described…
We study the hypermultiplet moduli space of the type II string compactified on a Calabi-Yau space $\bX$. We do this by using IIA/IIB duality in a compactification of the same theory on $\bX\times \bS ^1$ and by using recent results on three…
In this paper we investigate the properties of series of vacua in the string theory landscape. In particular, we study minima to the flux potential in type IIB compactifications on the mirror quintic. Using geometric transitions, we embed…
The simplest toroidally compactified string theories exhibit a duality between large and small radii: compactification on a circle, for example, is invariant under R goes to 1/R. Compactification on more general Lorentzian lattices (i.e.…
We examine spectrum of the physical volume operator within the non-standard loop quantum cosmology. The spectrum is discrete with equally distant levels defining a quantum of the volume. The discreteness may imply a foamy structure of…
Kaluza--Klein compactification in quantum field theory is analysed from the perturbation theory viewpoint. Renormalisation group analysis for compactification size dependence of the coupling constant is proposed.
Calabi-Yau spaces, or Kahler spaces admitting zero Ricci curvature, have played a pivotal role in theoretical physics and pure mathematics for the last half-century. In physics, they constituted the first and natural solution to…
The nature of space-time at high energy is an open question and the link between extra-dimensional theories with the physics of the Standard Model can not be established in a unique way. The compactification path is not unique and…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
The concept of quantization consists in replacing commutative quantities by noncommutative ones. In mathematical language an algebra of continuous functions on a locally compact topological space is replaced with a noncommutative…
With a bird's-eye view, we survey the landscape of Calabi-Yau threefolds, compact and non-compact, smooth and singular. Emphasis will be placed on the algorithms and databases which have been established over the years, and how they have…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
We discuss the classical and quantum reduction to the space of physical degrees of freedom of Yang--Mills theory on a circle (so that space-time is a cylinder). Although the classical reduced phase space is finite-dimensional, the quantum…