Related papers: The Heuristic Function of Duality
Most of the approaches to the construction of a theory of quantum gravity share some principles which do not have specific experimental support up to date. Two of these principles are relevant for our discussion: (i) the gravitational field…
Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
New actions in D=2 and D=3 are proposed that are dual equivalent to known theories displaying well defined chirality and helicity, respectively, along with a new interpolating action that maps continuously through the original dualities.…
The double copy formalism provides an intriguing connection between gauge theories and gravity. It was first demonstrated in the perturbative context of scattering amplitudes but recently the formalism has been applied to exact classical…
One of the basic observations of the classical world is that physical entities are real and can be distinguished from each other. However, within quantum theory, the idea of physical realism is not well established. A framework to analyse…
Analogies have had and continue to have an important role in the development of theoretical physics. They may start from similarities of physical concepts followed by similarities in the mathematical formalization or it may be a purely…
A "quantum-first" approach to gravity is described, where rather than quantizing general relativity, one seeks to formulate the physics of gravity within a quantum-mechanical framework with suitably general postulates. Important guides are…
Polar duality is a well-known concept from convex geometry and analysis. In the present paper, we study two symplectically covariant versions of polar duality keeping in mind their applications to quantum mechanics. The first variant makes…
I contrast two possible attitudes towards a given branch of physics: as inferential (i.e., as concerned with an agent's ability to make predictions given finite information), and as dynamical (i.e., as concerned with the dynamical equations…
Guided primarily by versions of a theoretical framework called Doubly Special Relativity, or DSR, that are supposed to entail speeds of light that vary with energy while preserving the relativity of inertial frames, quantum-gravity…
The search for a new scientific theory is typically prompted by an encounter with something in the world that cannot be explained by current theories. This is not the case for the search for a theory of quantum gravity, which has been…
As a canonical and generally covariant gauge theory, loop quantum gravity requires special techniques to derive effective actions or equations. If the proper constructions are taken into account, the theory, in spite of considerable…
The Quantum Hall Effects offer a rich variety of theoretical and experimental advances. They provide interesting insights on such topics as complementarity, gauge invariance, strong interactions, emergence of new theoretical concepts. This…
This book is not meant to be another compendium of select inequalities, nor does it claim to contain the latest or the slickest ways of proving them. This project is rather an attempt at describing how most functional inequalities are not…
The two dimensional substructure of general relativity and gravity, and the two dimensional geometry of quantum effect by black hole are disclosed. Then the canonical quantization of the two dimensional theory of gravity is performed. It is…
While philosophy of science is the study of problems of knowledge concerning science in general, there also exists - or should exist - a '' philosophy in science'' directed at finding out in what ways our actual scientific knowledge may…
We show that the Einstein equations in the vacuum are invariant under an $SO(2)$ duality symmetry which rotates the curvature 2-form into its tangent space Hodge dual. Akin to electric-magnetic duality in gauge theory, the duality operation…
We study in detail the space of perturbations of a pair of dual $N=1$ supersymmetric theories based on an $SU(N_c)$ gauge theory with an adjoint $X$ and fundamentals with a superpotential which is polynomial in $X$. The equivalence between…
We review quantitative tests on the duality between the heterotic string on T^2 and F-theory on K3. On the heterotic side, certain threshold corrections to the effective action can be exactly computed at one-loop order, and the issue is to…