TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Abstract: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics.
TL;DR: In this article, a new framework for solving the hierarchy problem has been proposed which does not rely on low energy supersymmetry or technicolor, and this framework can be embedded in string theory.
TL;DR: In this article, a superstring theory for E 8 × 8 × E 8 has been constructed, based on SO(32) and the remaining pieces of all the anomalies cancel if the gauge group is SO (32) or E 8×E 8.
TL;DR: In this paper, the authors studied candidate vacuum configurations in ten-dimensional O(32) and E 8 × E 8 supergravity and superstring theory that have unbroken N = 1 supersymmetry in four dimensions.
TL;DR: In this article, a new framework for solving the hierarchy problem has been proposed which does not rely on low energy supersymmetry or technicolor, and this framework can be embedded in string theory.
Abstract: Recently, a new framework for solving the hierarchy problem has been proposed which does not rely on low energy supersymmetry or technicolor. The gravitational and gauge interactions unite at the electroweak scale, and the observed weakness of gravity at long distances is due the existence of large new spatial dimensions. In this letter, we show that this framework can be embedded in string theory. These models have a perturbative description in the context of type I string theory. The gravitational sector consists of closed strings propagating in the higher-dimensional bulk, while ordinary matter consists of open strings living on D3-branes. This scenario raises the exciting possibility that the LHC and NLC will experimentally study both ordinary aspects of string physics such as the production of narrow Regge-excitations of all standard model particles, as well more exotic phenomena involving strong gravity such as the production of black holes. The new dimensions can be probed by events with large missing energy carried off by gravitons escaping into the bulk. We finally discuss some important issues of model building, such as proton stability, gauge coupling unification and supersymmetry breaking.