Let M̃ be a (2m+ 1)-dimensional almost contact manifold with almost contact structure (φ,ξ,η), that is, a global vector field ξ, a (1,1) tensor field φ, and a 1-form η on M̃ such that φ2X =−X +η(X)ξ, η(ξ) = 1 for any vector field X on M̃. We consider a product manifold M̃×R, whereR denotes a real line. Then a vector field on M̃×R is given by (X , f (d/dt)), where X is a vector field tangent to M̃, t ...

A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl’s electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the conformal connection. By showing that every one-particle Hamiltonian generates the structure equations we establish a correspondence between phase space and the 8-d...

Two-dimensional exactly solvable loop models, built on the Temperley-Lieb algebra, have previously been introduced to study statistical systems with non-local degrees of freedom such as polymers and percolation. In the continuum scaling limit, these models describe logarithmic minimal Conformal Field Theories (CFTs). In this thesis, we introduce and study new two-dimensional exactly solvable su...

The prevalent theory of cosmological inflation, which attempts to explain the high degree of isotropy observed from the Earth’s location in the Universe, has been criticised for being ad hoc and thermodynamically unsound. A viable alternative to inflation is the combined theory of quiescent cosmology and the Weyl curvature hypothesis, in which cosmological models are studied within a mathematic...

In a short review of recent work, we discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. Such a construction follows when the old conformal field theory admits new conformal stress tensors in its chiral algebra, and it turns out that the new conformal field theory is generically a new spin-two gauge theory. As an example we ...

We show that holographic models of QCD predict the presence of a Chern-Simons coupling between vector and axial-vector mesons at finite baryon density. In the Anti de Sitter/Conformal Field Theory dictionary, the coefficient of this coupling is proportional to the baryon number density and is fixed uniquely in the five-dimensional holographic dual by anomalies in the flavor currents. For the li...

We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted R × R-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over V L ⊗ V R , where V L and V R are two vertex operat...