High Energy Physics

The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. In this talk I will describe a new method to study these models in the M-theory limit, but at all orders in the 1/N expansion. The method is based on reformulating the matrix model as the partition function of a Fermi gas. This new approach leads to a completely elementary derivation of the N^{3/2} behavior for ABJM theory and other quiver Chern-Simons-matter theories. In addition, the full series of 1/N corrections to the original matrix integral can be simply determined by a next-to-leading calculation in the semiclassical expansion of the quantum gas.

We investigate the theoretical implications of scale without conformal invariance in quantum field theory. We argue that the RG flows of such theories correspond to recurrent behaviors, i.e. limit cycles or ergodicity. We discuss the implications for the a-theorem and show how dilatation generators do generate dilatations. Finally, we discuss possible well-behaved non-conformal scale-invariant examples.

I will discuss magnetic properties of superconductors, first in a model independent way and then by using holographic models. This approach has the advantage of highlighting the generic features of superconducting materials and, at the same time, the predictions of specific models. I will start with the Meissner effect and the vortices. Given the importance of the magnetic field dynamics in these phenomena, I will describe how to introduce a dynamical gauge field in holography. Then I will show that the holographic superconductor, like all known high-temperature superconductors, is Type II. Finally, I will discuss the case of hollow cylindrical superconductors threaded by an axial magnetic field. The physics of these systems is periodic with respect to the magnetic flux, with a period that depends on weather non-local quantum effects are suppressed or not. In the holographic model these effects are not suppressed when the radius of the cylinder is below the critical value at which the Hawking-Page phase transition takes place.

In this talk I will give an overview of localization and some of its applications for QFTs in three dimensions. I will start by reviewing the localization procedure for N=2 supersymmetric gauge theories in three dimensions on S^3. I will then describe some of the applications to field theory dualities and to holography, and the possibility of extracting information about RG fixed points from the localized partition function.