Arrows in this diagram indicate input from one topic to another. Closely related topics are joined by lines. Conformal geometry is highly analogous to CR geometry, so their boxes are close together and arrows run in both directions. The left hand side of the diagram is largely algebraic. At the top of the diagram, Q-curvature and ambient metrics are specific aspects of conformal geometry, which...

In this paper it is argued that a Carter–Penrose diagram can be viewed as a differential space.

— The morphology of vesicles with topological genus g = 2 is studied using the properties of Willmore surfaces together with the conformal invariance of the bending energy of fluid membranes. In the phase diagram of the bilayer couple model, a region exists where vesicle shapes are given by Willmore surfaces. Within this region, shapes in general have no mirror symmetries and the ground state i...

We consider Quantum Toda theory associated to a general Lie algebra. We prove that the conserved quantities in both conformal and affine Toda theories exhibit duality interchanging the Dynkin diagram and its dual, and inverting the coupling constant. As an example we discuss the conformal Toda theories based on B2, B3 and G2 and the related affine theories. Feb 1992 1Email: H G [email protected]....

A new family of exactly solvable models is introduced. These models are generalizations of the XXZ chain where the distance among spins up (σ z-basis) cannot be smaller or equal to t (t = 0, 1, 2, ...). The case t = 0 recovers the standard XXZ chain. The coordinate Bethe ansatz is applied and the phase diagram is calculated. Exploring the finite-size consequences of conformal invariance the cri...

The knowledge of the phase diagram of strongly coupled theories as function of the number of colors, flavors and matter representation plays a fundamental role when constructing viable extensions of the standard model (SM) featuring dynamical electroweak symmetry breaking. Here I summarize the state-of-the-art of the phase diagram for SU(N) gauge theories with fermionic matter transforming acco...