Related papers: Breaking symmetry, breaking ground
We study necessary conditions on the geometry and the topology of domains in $\mathbb{R}^2$ that support a positive solution to a classical overdetermined elliptic problem. The ideas and tools we use come from constant mean curvature…
A brief discussion is presented assessing the achievements and challenges of string phenomenology: the subfield dedicated to study the potential for string theory to make contact with particle physics and cosmology. Building from the well…
I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…
We comment on the presence of spurious observables and on a subtle violation of irreducibility in loop quantum cosmology.
In this note we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten for superstring perturbation theory in arXiv:1209.5461. We intend to make the construction…
In this thesis we discuss some topics about topology and superstring backgrounds with D-branes. We start with a mathematical review about generalized homology and cohomology theories and the Atiyah-Hirzebruch spectral sequence, in order to…
This is a review article for The Review of Particle Physics 2006 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters as at May 2006. Topics included are Parametrizing the Universe; Extensions…
This is a comment on arXiv:1402.6767 (2014) by Y. Imura, T. Okubo, S. Morita, and K. Okunishi.
The intersection of string theory with cosmology is unavoidable in the early universe, and its exploration may shine light on both fields. In this thesis, three papers at this intersection are presented and reviewed, with the aim of…
In the past decade, observational cosmology has had one of the most exciting periods in the past century. The precision with which we have been able to measure cosmological parameters has increased tremendously, while at the same time, we…
Combining intervals of ekpyrotic (ultra-slow) contraction with a (non-singular) classical bounce naturally leads to a novel cyclic theory of the universe in which the Hubble parameter, energy density and temperature oscillate periodically,…
Dirac fermions in $2+1$ dimensions with dynamically generated anticommuting SO(3) antiferromagnetic (AFM) and Z$_2$ Kekul\'e valence-bond solid (KVBS) masses map onto a field theory with a topological $\theta$-term. This term provides a…
In cosmological scenarios based on grand unification, string theory or braneworlds, many kinds of topological or non-topological defects, including monopoles and cosmic strings, are predicted to be formed in the early universe. Here we…
An old branch of mathematics, Topology, has opened the road to the discovery of new phases of matter. A hidden topology in the energy spectrum is the key for novel conducting/insulating properties of topological matter.
Questions such as whether we live in a spatially finite universe, and what its shape and size may be, are among the fundamental open problems that high precision modern cosmology needs to resolve. These questions go beyond the scope of…
We give a leisurely, albeit woefully incomplete, overview of quantum field theory, its relevance to condensed matter systems, and spin systems, which proceeds via a series of illustrative examples. The goal is to provide readers from the…
We illustrate a physical situation in which topological symmetry, its breakdown, space-time uncertainty principle, and background independence may play an important role in constructing and understanding matrix models. First, we show that…
The 1983 book, free at last, with corrections and bookmarks. From the original troff, but now with CM (TeX) fonts.
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…
In this Reply, using E.R. Bezerra de Mello's comment, I correct calculations and results presented in Phys. Lett. B 614 (2005) 140-142 about fine structure constant in the spacetime of a cosmic string.