Related papers: Dynamical Lorentz symmetry breaking and topologica…
We construct supersymmetric K field theories (i.e., theories with a non-standard kinetic term) in 1+1 and 2+1 dimensions such that the bosonic sector just consists of a nonstandard kinetic term plus a potential. Further, we study the…
We demonstrate that five-dimensional, asymptotically flat, stationary and biaxisymmetric, vacuum black holes with lens space $L(n, 1)$ topology, possessing the simplest rod structure, do not exist. In particular, we show that the general…
We construct compact initial data of constant mean curvature $\widetilde{K}$ for Einstein's 4d vacuum equations with $\widehat{\Lambda} = \Lambda - (\widetilde{K}^2/3)$ positive, where $\Lambda$ is the cosmological constant, via the…
It is known that if gauge conditions have Gribov zero modes, then topological symmetry is broken. In this paper we apply it to topological gravity in dimension $n \geq 3$. Our choice of the gauge condition for conformal invariance is…
In this paper we study the locus of singular tuples of a complex valued multisymmetric tensor. The main problem that we focus on is: given the set of singular tuples of some general tensor, which are all the tensors that admit those same…
We review some of the basic features and predictions of a gauge invariant spontaneous Lorentz symmetry breaking model arising from the nonzero vacuum expectation value of the electromagnetic tensor and leading to a nonlinear…
The field equations of a special class of teleparallel theory of gravitation and electromagnetic fields have been applied to tetrad space having cylindrical symmetry with four unknown functions of radial coordinate $r$ and azimuth angle…
Junction conditions for vacuum solutions in five-dimensional Einstein-Gauss-Bonnet gravity are studied. We focus on those cases where two spherically symmetric regions of space-time are joined in such a way that the induced stress tensor on…
Theories that spontaneously break Lorentz invariance also violate diffeomorphism symmetries, implying the existence of extra degrees of freedom and modifications of gravity. In the minimal model (``ghost condensation'') with only a single…
Considering rank s fields obey first order equation of motion, we study the dynamics of such fields in a 3 dimensional self-dual space-like warped $AdS_3$ black hole background. We argue that in this background, symmetric conditions and…
We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion…
There has been continued interest in seeking a theorem describing optimal low-rank approximations to tensors of order 3 or higher, that parallels the Eckart-Young theorem for matrices. In this paper, we argue that the naive approach to this…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
We obtain exact analytical solutions for a class of SO($l$) Higgs field theories in a non-dynamic background $n$-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric $p$-dimensional topological…
In these lectures, I review cosmological phase transitions and the topological aspects of spontaneous symmetry breaking. I then discuss the formation of walls, strings and monopoles during phase transitions including lattice based studies…
We introduce a new version of non-linear electrodynamics which is produced by a spontaneous symmetry breaking of Lorentz invariance induced by the non-zero expectation value of the electromagnetic field strength. The symmetry breaking…
We consider the mechanism of spontaneous symmetry breaking of a bulk vector field to study signatures of bulk dimensions invisible to the standard model confined to the brane. By assigning a non-vanishing vacuum expectation value to the…
A self consistent effective field theory of modified gravity has recently been proposed with spontaneous breaking of local Lorentz invariance. The symmetry is broken by a vector field with the wrong-sign mass term and it has been shown to…
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…
In this article, we study complete pseudo-Riemannian manifolds whose cone admits a parallel symmetric 2-tensorfield. The situation splits in three cases: nilpotent, decomposable or complex Riemannian. In the complex Riemannian and…