Related papers: Chiral Splitting at Work
We analyze the chiral operator ring of the symmetric orbifold conformal field theory on the complex two-plane. We compute the large N limit of the ring and exhibit its factorized leading order behaviour. We moreover calculate all structure…
This note records some dilation theorems about contraction semigroups on a Hilbert space - all of which fall into the categories "known" or "probably known" - that I proved while working on my PhD in mathematics (under the supervision of…
Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form. In this paper, we do two things. First, we describe some broad features of systems of…
The solution of a class of third order ordinary differential equations possessing two parameter Lie symmetry group is obtained by group theoretic means. It is shown that reduction to quadratures is possible according to two scenarios: 1) if…
We present the operator semigroups approach to first- and second-order dynamical systems taking place on metric graphs. We briefly survey the existing results and focus on the well-posedness of the problems with standard vertex conditions.…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…
The adjoint action of a finite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are…
We present a general classification of all normal and ``chiral" symmetries of heavy quark effective theories. Some peculiarities and conondrums associated with the ``chiral" symmetries are discussed.
A theory of cyclic elements in semisimple Lie algebras is developed. It is applied to an explicit construction of regular elements in Weyl groups.
The equivariant movability of topological spaces with an action of a given topological group $G$ is considered. In particular, the equivariant movability of topological groups is studied. It is proved that a second countable group $G$ is…
We study a class of four-dimensional N=1 superconformal field theories obtained from the six-dimensional (1,0) theory, on M5-branes on C^2/Z_k orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge…
We study half-BPS surface operators in supersymmetric gauge theories in four and five dimensions following two different approaches. In the first approach we analyze the chiral ring equations for certain quiver theories in two and three…
We derive several versions of the cell theory for a crystal phase of hard equilateral triangles. To that purpose we analytically calculated the free area of a frozen oriented or freely rotating particle inside the cavity formed by its…
The chiral model for self-dual gravity given by Husain in the context of the chiral equations approach is discussed. A Lie algebra corresponding to a finite dimensional subgroup of the group of symplectic diffeomorphisms is found, and then…
In the figure-eight choreography in the classical three-body problem, both-side bifurcation solutions sometimes fold on one side of the bifurcation point with cusp of action. Three numerical examples of a such fold for figure-eight…
Questions of the following sort are addressed: Does a given Lie group or Lie algebra act effectively on a given manifold? How smooth can such actions be? What fxed-point sets are possible? What happens under perturbations? Old results are…
Lie groups considered as three-dimensional almost paracontact almost paracomplex Riemannian manifolds are investigated. In each basic class of the classification used for the manifolds under consideration, a correspondence is established…
A general way of interpreting odd dimensional models as a doublet of chiral models is discussed. Based on the equations of motion this dual composition is illustrated. Examples from quantum mechanics, field theory and gravity are…
We give an extension of Cheeger's deformation techniques for smooth Lie group actions on manifolds to the setting of singular Riemannian foliations induced by Lie groupoids actions. We give an explicit description of the sectional curvature…