Duality Symmetry

Symmetry is one of the most general concepts in physics. Symmetry arguments are used to explain and predict observations at all length scales, from elementary particles to cosmology. The generality of symmetry arguments, combined with their simplicity, makes them a powerful tool for both fundamental and applied investigations. In electrodynamics, one of the symmetries is the invariance of the equations under exchange of electric and magnetic quantities. The continuous version of this symmetry is most commonly known as electromagnetic duality symmetry. This concept has been accepted for more than a century, and, throughout this time, has influenced other areas of physics, like high energy physics and gravitation. This Special Issue is devoted to electromagnetic duality symmetry and other vareities of dualities in physics. It contains four Articles, one Review and one Perspective. The context of the contributions ranges from string theory to applied nanophotonics, which, as anticipated, shows that duality symmetries in general and electromagnetic duality symmetry in particular are useful in a wide variety of physics fields, both theoretical and applied. Moreover, a number of the contributions show how the use of symmetry arguments and the quantification of symmetry breaking can successfully guide our theoretical understanding and provide us with guidelines for system design.

The contributions to this volume of the famous summer school in Les Houches cover the recent developments in supersymmetric string theory, the gauge theory/string theory correspondence and string duality. The book is a comprehensive introduction to the recent developments in string/M-theory and quantum gravity.

This is the first systematic introduction to electromagnetic duality and its generalisations. The authors are the leading figures in this exciting new area of mathematical physics, and their lectures have been organised not only to link with each other but also to describe the fundamental ideas, the latest developments, and some earlier work whose significance has only recently become apparent. This will be essential reading for all those working in mathematical physics.

Symmetry is one of the most general concepts in physics. Symmetry arguments are used to explain and predict observations at all length scales, from elementary particles to cosmology. The generality of symmetry arguments, combined with their simplicity, makes them a powerful tool for both fundamental and applied investigations. In electrodynamics, one of the symmetries is the invariance of the equations under exchange of electric and magnetic quantities. The continuous version of this symmetry is most commonly known as electromagnetic duality symmetry. This concept has been accepted for more than a century, and, throughout this time, has influenced other areas of physics, like high energy physics and gravitation. This Special Issue is devoted to electromagnetic duality symmetry and other vareities of dualities in physics. It contains four Articles, one Review and one Perspective. The context of the contributions ranges from string theory to applied nanophotonics, which, as anticipated, shows that duality symmetries in general and electromagnetic duality symmetry in particular are useful in a wide variety of physics fields, both theoretical and applied. Moreover, a number of the contributions show how the use of symmetry arguments and the quantification of symmetry breaking can successfully guide our theoretical understanding and provide us with guidelines for system design.

Teleparallel Gravity (TG) is an alternative theory for gravitation, which is equivalent to General Relativity (GR). However, it is conceptually different. For example in GR geometry replaces the concept of force, and the trajectories are determined by geodesics. TG attributes gravitation to torsion, which accounts for gravitation by acting as a force. TG has already solved some old problems of gravitation (like the energy-momentum density of the gravitational field). The interest in TG has grown in the last few years. The book here proposed will be the first one dedicated exclusively to TG, and will include the foundations of the theory, as well as applications to specific problems to illustrate how the theory works.

This proceedings volume covers the main fields of mathematics: analysis, algebra and number theory, geometry and topology, combinatorics and graphs, applied mathematics, numerical analysis and computer mathematics, probability and statistics, teaching and popularization of mathematics.

This book is a pedagogical introduction to supergravity, a gravitational field theory that includes supersymmetry (symmetry between bosons and fermions) and is a generalization of Einstein's general relativity. Supergravity provides a low-energy effective theory of superstring theory, which has attracted much attention as a candidate for the unified theory of fundamental particles, and it is a useful tool for studying non-perturbative properties of superstring theory such as D-branes and string duality. This work considers classical supergravities in four and higher spacetime dimensions with their applications to superstring theory in mind. More concretely, it discusses classical Lagrangians (or field equations) and symmetry properties of supergravities. Besides local symmetries, supergravities often have global non-compact symmetries, which play a crucial role in their applications to superstring theory. One of the main features of this book is its detailed discussion of these non-compact symmetries. The aim of the book is twofold. One is to explain the basic ideas of supergravity to those who are not familiar with it. Toward that end, the discussions are made both pedagogical and concrete by stating equations explicitly. The other is to collect relevant formulae in one place so as to be useful for applications to string theory. The subjects discussed in this book include the vielbein formulation of gravity, supergravities in four dimensions, possible types of spinors in various dimensions, superalgebras and supermultiplets, non-linear sigma models for non-compact Lie groups, electric-magnetic duality symmetries, supergravities in higher dimensions, dimensional reductions, and gauged and massive supergravities.