Conference

Magnetic fields are ubiquitous in our Universe. The are observed in galaxies and clusters in our vicinity and at high redshifts. In my talk I outline the possibilities to generate magnetic fields in the early Universe during inflation or during a first order phase transition. I explain the form of the magnetic field spectrum obtained in the different cases. I also discuss the subsequent evolution of helical and non-helical magnetic fields in the cosmological plasma and argue that fields generated at the electroweak phase transition do not have enough large scale power to represent the magnetic fields observed in galaxies and clusters, even if they are maximally helical.

I'll discuss some work done in collaboration with Cliff Burgess, Louis Leblond and Sarah Shandera on the significance of the IR divergences in de Sitter space. First, I'll talk about how large fluctuations at long distances can induce the failure of the loop expansion for interacting field theories with massless degrees of freedom in de Sitter space, much in the same manner as happens in thermal field theories. Then I'll shift gears slightly and describe work involving the use of the dynamical renormalization group in resumming the secularly growing perturbative corrections to correlation functions for massless, minimally coupled scalar fields in de Sitter.

We discuss holographic models for the inflationary epoch. We show how cosmological observables such as the primordial spectrum and non-Gaussianities can be computed via computations of correlation functions of a dual three dimensional QFT (without gravity!) We present a general class of models that have the following universal features: (i) they have a nearly scale invariant spectrum of small amplitude primordial fluctuations, (ii) the scalar spectral index runs as alpha_s = - (n_s-1), (iii) the three point function of density perturbations is exactly equal to the sum of the local and equilateral form with f_{NL}^{local} = 6 f_{NL}^{equil} = 20/3.

I describe a novel abelian gauge theory in 2+1 dimensions which has surprising theoretical and phenomenological features. The theory has a vanishing coefficient for the square of the electric field $e_i^2$, characteristic of a quantum critical point with dynamical critical exponent $z=2$, and a level-$k$ Chern-Simons coupling, which is marginal at this critical point. For $k=0$, this theory is dual to a free $z=2$ scalar field theory describing a quantum Lifshitz transition, but $k \neq 0$ renders the scalar description non-local. The $k \neq 0$ theory exhibits properties intermediate between the (topological) pure Chern-Simons theory and the scalar theory. For instance, the Chern-Simons term does not make the gauge field massive. Nevertheless, there are chiral edge modes when the theory is placed on a space with boundary, and a non-trivial ground state degeneracy $k^g$ when it is placed on a finite-size Riemann surface of genus $g$. The coefficient of $e_i^2$ is the only relevant coupling; it tunes the system through a quantum phase transition between an isotropic fractional quantum Hall state and an anisotropic fractional quantum Hall state. I describe zero-temperature transport coefficients in both phases and at the critical point, and comment briefly on the relevance of the results to recent experiments.