Related papers: Unrectifiable normal currents in Euclidean spaces
For a spacetime of odd dimensions endowed with a unit vector field, we introduce a new topological current that is identically conserved and whose charge is equal to the Euler character of the even dimensional spacelike foliations. The…
Given a conserved and traceless energy-momentum tensor and a conformal Killing vector, one obtains a conserved current. We generalise this construction to superconformal theories in three, four, five and six dimensions with various amounts…
We prove that for every indecomposable ordinal there exists a (transfinitely valued) Euclidean domain whose minimal Euclidean norm is of that order type. Conversely, any such norm must have indecomposable type, and so we completely…
We introduce a method for reconstructing an infinitesimal normalizing flow given only an infinitesimal change to a (possibly unnormalized) probability distribution. This reverses the conventional task of normalizing flows -- rather than…
We re-examine the Klein paradox from a many-particle perspective in quantum field theory. Specifically, we compute the expectation value of the particle current induced by a sufficiently strong step-like electric potential in 1+1…
This paper proposes direct and inverse results for the Dirichlet and Dirichlet to Neumann problems for complex curves with nodal type singularities. As an application, we give a method to reconstruct the conformal structure of a compact…
As a first application of our renormalisation group approach to non-local matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean two-dimensional noncommutative \phi^4-theory. It is widely believed that this model is…
Positive vacuum energy together with extra dimensions of space imply that our four-dimensional Universe is unstable, generically to decompactification of the extra dimensions. Either quantum tunneling or thermal fluctuations carry one past…
One dimensional Dirac equation is analysed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the…
Multidimensional cosmological models in the presence of a bare cosmological constant and a perfect fluid are investigated under dimensional reduction to 4-dimensional effective models. Stable compactification of the internal spaces is…
I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson-Wegner renormalization group. I first consider massive Euclidean $\phi_4^4$-theory. The renormalization proofs are…
Let V be a simple VOA and consider a representation category of V that is a vertex tensor category in the sense of Huang-Lepowsky. In particular, this category is a braided tensor category. Let J be an object in this category that is a…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
We develop, via Arnold's geometric framework, a mechanism for constructing explicit, smooth, global-in-time, and typically non-stationary solutions of the incompressible Euler equations. The approach introduces a notion of generalized…
The relation between the trace and R-current anomalies in 4D supersymmetric theories implies that the U(1)$_R$F$^2$, U(1)$_R$ and U(1)$^3_R$ anomalies which matched in studies of N=1 Seiberg duality satisfy positivity constraints. These…
Non-conformal supercurrents in six dimensions are described, which contain the trace of the energy-momentum tensor and the gamma-trace of the supersymmetry current amongst their component fields. Within the superconformal approach to ${\cal…
In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure is carried out by constructing solutions to the following elliptic…
We examine the blow-up claims of the incompressible Euler equations for several specific flow-fields, (1) the columnar eddies in the vicinity of stagnation; (2) a quasi-three-dimensional structure for illustrating oscillations and…
We review extensions by integer spin simple currents in two-dimensional conformal field theories and their applications in string theory. In particular, we study the problem of resolving the fixed points of a simple current and apply the…
The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald's functions $K_{0}(b r)$ and $K_{1}(b r)$. This central…