We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of $\overline{\mathrm{D}3}$-branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is much greater than the cosmological time scale of ${10}^{10}\mathrm{yr}.$ We also prove, under certain conditions, that the lifetime of dS space in string theory will always be shorter than the recurrence time.

/pdf/de-sitter-vacua-in-string-theory-2gp3ty8kg8.pdf

De Sitter vacua in string theory

Phases of N = 2 theories in two dimensions

Over the 100 years since its discovery, liquid crystals have been the intriguing subject for both academia and industries. The textbook of de Gennes The Physics of Liquid Crystals published in 1974 is still the bible for many LC researchers, but new subjects unmentioned in the book have also risen for these years. This chapter describes the story of the recent developments and the future perspectives in physics of liquid crystals, especially focusing on the contributions by Japanese research groups for the last decade.

Physics of Liquid Crystals

http://cds.cern.ch/record/994225/files/0610327.pdf

Four-dimensional string compactifications with D-branes, orientifolds and fluxes

We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics We explain how this work implies that there is a ``landscape'' of string/M theory vacua, perhaps containing many candidates for describing real world physics, and present the arguments for and against this idea We discuss statistical surveys of the landscape, and the prospects for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking

Flux Compactification

Four dimensional reflexive polyhedra encode the data for smooth Calabi-Yau threefolds that are hypersurfaces in toric varieties, and have important applications both in perturbative and in non-perturbative string theory. We describe how we obtained all 473,800,776 reflexive polyhedra that exist in four dimensions and the 30,108 distinct pairs of Hodge numbers of the resulting Calabi-Yau manifolds. As a by-product we show that all these spaces (and hence the corresponding string vacua) are connected via a chain of singular transitions.

https://www.intlpress.com/site/pub/files/_fulltext/journals/atmp/2000/0004/0006/ATMP-2000-0004-0006-a002.pdf

Complete classification of reflexive polyhedra in four-dimensions

PALP: A Package for Analysing Lattice Polytopes with applications to toric geometry☆

We give a criterion for the existence of a non-degenerate quasihomogeneous polynomial in a configuration, i.e. in the space of polynomials with a fixed set of weights, and clarify the relation of this criterion to the necessary condition derived from the formula for the Poincare polynomial. We further prove finiteness of the number of configurations for a given value of the singularity index. For the value 3 of this index, which is of particular interest in string theory, a constructive version of this proof implies an algorithm for the calculation of all non-degenerate configurations.

/pdf/on-the-classification-of-quasihomogeneous-functions-3mrcu76ocg.pdf

On the classification of quasihomogeneous functions

We present the last missing details of our algorithm for the classification of reflexive polyhedra in arbitrary dimensions. We also present the results of an application of this algorithm to the case of three dimensional reflexive polyhedra. We get 4319 such polyhedra that give rise to K3 surfaces embedded in toric varieties. 16 of these contain all others as subpolyhedra. The 4319 polyhedra form a single connected web if we define two polyhedra to be connected if one of them contains the other.

https://www.intlpress.com/site/pub/files/_fulltext/journals/atmp/1998/0002/0004/ATMP-1998-0002-0004-a005.pdf

Classification of reflexive polyhedra in three-dimensions

We describe our package PALP of C programs for calculations with lattice polytopes and applications to toric geometry, which is freely available on the internet. 
It contains routines for vertex and facet enumeration, computation of incidences and symmetries, as well as completion of the set of lattice points in the convex hull of a given set of points. In addition, there are procedures specialised to reflexive polytopes such as the enumeration of reflexive subpolytopes, and applications to toric geometry and string theory, like the computation of Hodge data and fibration structures for toric Calabi-Yau varieties. 
The package is well tested and optimised in speed as it was used for time consuming tasks such as the classification of reflexive polyhedra in 4 dimensions and the creation and manipulation of very large lists of 5-dimensional polyhedra. 
While originally intended for low-dimensional applications, the algorithms work in any dimension and our key routine for vertex and facet enumeration compares well with existing packages.

Harald Skarke

Papers

Complete classification of reflexive polyhedra in four-dimensions

PALP: A Package for Analysing Lattice Polytopes with applications to toric geometry☆

On the classification of quasihomogeneous functions

Classification of reflexive polyhedra in three-dimensions

PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry