Related papers: Notes On Supermanifolds and Integration
We discuss in detail the symmetry breaking and related issues in the minimal renormalizable supersymmetric grand unified theory. We compute the particle spectrum and study its impact on the physical scales of the theory. This provides a…
This review is devoted to strings and branes. Firstly, perturbative string theory is introduced. The appearance of various types of branes is discussed. These include orbifold fixed planes, D-branes and orientifold planes. The connection to…
The purpose of these notes is to give a brief review of superfluidity in neutron stars. After a short presentation explaining why and how superfluidity is expected in the crust and core of neutron stars, consequences on thermal evolution…
The subfactor approach to modular invariants gives insight into the fusion rule structure of the modular invariants.
An overview of string theory in the maximally supersymmetric plane-wave background is given, and some supersymmetric D-branes are discussed.
A recollection of some theoretical developments that preceded and followed the first formulation of supergravity theory is presented. Special emphasis is placed on the impact of supergravity on the search for a unified theory of fundamental…
In this paper, we introduce the notion of a super tangent bundle of a manifold, and extend the basic notions of differential geometry such as differential forms, exterior derivation, connection, metric and divergence on manifolds that…
The SO(32) heterotic superstring on a Calabi-Yau manifold can spontaneously break supersymmetry at one-loop order even when it is unbroken at tree-level. It is known that calculating the supersymmetry-breaking effects in this model gives a…
Two-dimensional sigma-models describing superstrings propagating on manifolds of special holonomy are characterized by symmetries related to covariantly constant forms that these manifolds hold, which are generally non-linear and close in a…
We study the Hadamard finite part of divergent integrals of differential forms with singularities on submanifolds. We give formulae for the dependence of the finite part on the choice of regularization and express them in terms of a…
In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation…
We review the status of duality symmetries in superstring theories. These discrete symmetries mark the striking differences between theories of pointlike objects and theories of extended objects. They prove to be very helpful in…
Various aspects of Supersymmetry in 1-dimensional systems are analyzed.
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is argued that any representation can be given as a superfield on many superflag manifolds. Representations on analytic superspaces do not…
We begin with a brief discussion of the building blocks of supersymmetric grand unified theories. We recall some of the compelling theoretical reasons for viewing supersymmetric grand unification as an attractive avenue for physics beyond…
In these lectures we give a brief introduction to perturbative and non-perturbative string theory. The outline is the following: 1. Introduction to perturbative string theory 1.1 From point particle to extended objects 1.2 Free closed and…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
The holomorphy of the superpotential along with symmetries gives very strong constraints on any stringy non-perturbative effects. This observation suggests an approach to string phenomenology. (Presented at ``Strings 95'', March 1995.
A review of the superstatistics concept is provided, including various recent applications to complex systems.
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…