Related papers: Singularities and diffeomorphisms
We propose a higher dimensional scenario to solve the gauge hierarchy problem. In our formulation, a crucial observation is that a supersymmetric structure is hidden in the 4d spectrum of any gauge invariant theories with compact extra…
Transverse Diffeomorphism (TDiff) theories are well-motivated theories of gravity from the quantum perspective, which are based upon a gauge symmetry principle. The main contribution of this work is to firmly establish a correspondence…
Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine…
Partial differential equations (PDEs) with spatially-varying coefficients arise throughout science and engineering, modeling rich heterogeneous material behavior. Yet conventional PDE solvers struggle with the immense complexity found in…
The gauge symmetry is said unfree if the gauge transformation leaves the action functional unchanged provided for the gauge parameters are constrained by the system of partial differential equations. The best known example of this…
A brief overview of dimensional reductions for diffeomorphism invariant theories is given. The distinction between the physical idea of compactification and the mathematical problem of a consistent truncation is discussed, and the typical…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
We study the gauge invariance of physical observables in holographic theories under the local diffeomorphism. We find that gauge invariance is intimately related to the holographic renormalisation: the local counter terms defined in the…
In this book chapter we study the Riemannian Geometry of the density registration problem: Given two densities (not necessarily probability densities) defined on a smooth finite dimensional manifold find a diffeomorphism which transforms…
Modern geometric measure theory, developed largely to solve the Plateau problem, has generated a great deal of technical machinery which is unfortunately regarded as inaccessible by outsiders. Some of its tools (e.g., flat norm distance and…
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…
We extend to larger unification groups an earlier study exploring the possibility of unification of gauge symmetries in theories with dynamical symmetry breaking. Based on our results, we comment on the outlook for models that seek to…
General Relativity can be reformulated as a diffeomorphism invariant SU(2) gauge theory. A new action principle for this "pure connection" formulation of GR is described.
We study a long-recognised but under-appreciated symmetry called "dynamical similarity" and illustrate its relevance to many important conceptual problems in fundamental physics. Dynamical similarities are general transformations of a…
We prove compactness of solutions of a fully nonlinear Yamabe problem satisfying a lower Ricci curvature bound, when the manifold is not conformally diffeomorphic to the standard sphere. This allows us to prove the existence of solutions…
In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition -- an issue resolved by the observation…
The EPDiff equation governs geodesic flow on the diffeomorphisms with respect to a chosen metric, which is typically a Sobolev norm on the tangent space of vector fields. EPDiff admits a remarkable ansatz for its singular solutions, called…
All gauge theories need ``something fixed'' even as ``something changes.'' Underlying the implementation of these ideas all major physical theories make indispensable use of an elaborately designed spacetime model as the ``something…
Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This theory has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge…
We first consider M-theory formulated on an open eleven-dimensional spin-manifold. There is then a potential anomaly under gauge transformations on the E_8 bundle that is defined over the boundary and also under diffeomorphisms of the…