Conformal Invariance of Graphene Sheets

Conformal Invariance of Graphene Sheets

Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent 0.72 ± 0.01. Here, we show that, independent of the temperature, the iso-height lines at the percolation threshold have a well-defined fractal dimension and are conformally invariant, sharing the same statistical properties as Schramm-Loewn...

Conformal invariance from non-conformal gravity

We discuss the conditions under which classically conformally invariant models in four dimensions can arise out of non-conformal (Einstein) gravity. As an ‘existence proof’ that this is indeed possible we show how to derive N = 4 super Yang Mills theory with any compact gauge group G from non-conformal gauged N = 4 supergravity as a special flat space limit. We stress the role that the anticipa...

Chapter 18 Conformal Invariance

At the beginning of the semester we motivated our investigation of symmetries by illustrating that, given differential equations which were symmetric, the solutions had to transform into each other under the symmetries as a representation of the symmetry. The first illustrations considered Schrödinger equations with symmetric potentials, such as the electrons in the spherically symmetric potent...

Conformal invariance of domino tiling

Conformal Invariance of Voronoi Percolation

It is proved that in the Voronoi model for percolation in dimension 2 and 3, the crossing probabilities are asymptotically invariant under conformal change of metric. To deene Voronoi percolation on a manifold M , you need a measure , and a Riemannian metric ds. Points are scattered according to a Poisson point process on (M;), with some density. Each cell in the Voronoi tessellation determined...