Harrison-Zeldovich spectrum from conformal invariance

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...

Distortions of the Harrison-Zel’dovich spectrum from the QCD transition

We investigate the effect of the cosmological QCD transition on the evolution of primordial density perturbations. If the phase transition is first order, the sound speed vanishes during the transition and density perturbations fall freely. The Harrison-Zel’dovich spectrum of density fluctuations develops large peaks on scales below the Hubble radius at the transition. These peaks above the pri...

Conformal Invariance and Integrable Theories

Integrable theories on the lattice having zero energy gap exhibit conformal invariance for long distances. It is shown here how to extract its conformal properties (central charge e and scaling dimensions) from the Bethe ansatz equations. The methods here exposed are applied to the six-vertex model and to the critical Potts model.

Conformal invariance of domino tiling