Related papers: Sharpened Dynamical Cobordism
We argue that any proposed quantum theory of gravity with non-trivial cobordism classes in the space of configurations belongs to the Swampland. The argument is based on the assumption that there are no global symmetries in a consistent…
We consider the M-theory lifts of configurations of type IIA D6-branes intersecting at angles. In supersymmetry preserving cases, the lifts correspond to special holonomy geometries, like conifolds and $G_2$ holonomy singularities.…
In recent years there has been growing interest in verifying the horizon-scale homogeneity of the Universe that follows from applying the Copernican Principle to the observed isotropy. This program has been stimulated by the discovery that…
We investigate sensitivity to cumulative perturbations for a few dynamical system classes of practical interest. A system is said to have bounded sensitivity to cumulative perturbations (bounded sensitivity, for short) if an additive…
The deformation theory of singular varieties plays a central role in understanding the geometry and moduli of algebraic varieties. For a variety $X$ with possibly singular points, the space of first-order infinitesimal deformations is given…
In mechanical systems it is of interest to know the onset of fracture in dependence of the boundary conditions. Here we study a one-dimensional model which allows for an underlying heterogeneous structure in the discrete setting. Such…
We investigate the black hole - string transition in the two-dimensional Lorentzian black hole system from the exact boundary states that describe the rolling D-brane falling down into the two-dimensional black hole. The black hole - string…
We develop a model of spatially flat, homogeneous and isotropic cosmology in Lorentzian Regge calculus, employing 4-dimensional Lorentzian frusta as building blocks. By examining the causal structure of the discrete spacetimes obtained by…
Investigating the dynamics of gravitational systems, especially in the regime of quantum gravity, poses a problem of measuring time during the evolution. One of the approaches to this issue is using one of the internal degrees of freedom as…
For a general discrete dynamics on a Banach and Hilbert spaces we give a necessary and sufficient conditions of the existence of bounded solutions under assumption that the homogeneous difference equation admits an exponential dichotomy on…
We revisit an effective space-time torsion curvature in a second order formalism, underlying the non-linear $U(1)$ gauge dynamics, of a two form on a $D_4$-brane in type IIA superstring theory. The formalism incorporates the significance of…
It is well known that the dynamical mechanism of decoherence may cause apparent superselection rules, like that of molecular chirality. These `environment-induced' or `soft' superselection rules may be contrasted with `hard' superselection…
In extensions of general relativity and in theories aiming at unifying gravity with the forces of the Standard Model, the value of the "fundamental constants" is often determined by the vacuum expectation value of new fields, which may thus…
We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general…
Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory…
We present a status report on a discrete approach to the the near-equilibrium statistical theory of three-dimensional turbulence, which generalizes earlier work by no longer requiring that the vorticity field be a union of discrete vortex…
Sharply o-minimal structures (denoted \so-minimal) are a strict subclass of the o-minimal structures, aimed at capturing some finer features of structures arising from algebraic geometry and Hodge theory. Sharp o-minimality associates to…
This paper deals with the problem of global solvability and boundedness of classical solutions to a fully parabolic chemotaxis system with singular sensitivity in any dimensional setting. In particular, We show that the system…
Under reasonable assumptions about the complex structure of the set of singularities on the Coulomb branch of $\mathcal N=2$ superconformal field theories, we present a relatively simple and elementary argument showing that the scaling…
Dynamical cobordisms implement the swampland cobordism conjecture in the framework of effective field theory, realizing codimension 1 end of the world (ETW) branes as singularities at finite spacetime distance at which scalars diverge to…