We show that supersymmetry is anomalous in N = 1 superconformal quantum field theories (SCFTs) with an anomalous R-symmetry. This anomaly was originally found in holographic theories: here we show that this anomaly is present in general and demonstrate it for the massless superconformal Wess-Zumino model via a one loop computation of four-point functions of two supercurrents with either R-currents. In fact, the Wess-Zumino consistency conditions together with the standard R-symmetry anomaly imply the existence of the anomaly. We outline the implications of this anomaly.

In recent years there has ben considerable interest in using holographic methods to model strongly interacting condensed matter systems, including unconventional superconductors. However, many high Tc superconductors exhibit d-wave pairing and a satisfactory holographic realization of d-wave superconductors has been elusive. In this talk we will present a top down model for d-wave superconductors and discuss its phenomenology.

Abstract: There has recently been considerable discussion of holographic backgrounds with Schrodinger and Lifshitz symmetry, motivated by condensed matter applications. Since the bulk spacetimes are not asymptotically AdS, there are however many subtleties in setting up a holographic dictionary. In this talk we will argue that Schrodinger spacetimes (along with some realizations of Lifshitz) can be understood in terms of deformations of conformal field theories which break the relativistic scaling symmetry, but preserve an anisotropic/non-relativistic scale symmetry. We will highlight how this fact restricts which condensed matter systems can be well modeled holographically, and we will briefly discuss how the entropy of Schrodinger black holes (so-callsed null warped black holes) in three dimensions can be understood in this framework.

In the first part of the talk we discuss how to construct geometries sourced by branes carrying general condensates. As an example we consider fundamental strings carring fermion bilinear condensates. Dualizing to the D1-D5 system these correspond to the missing geometries needed to account for all black hole microstates in the fuzzball conjecture. In the second half of the talk we discuss new results in extracting field theory data from (asymptotically AdS) geometries. These methods can be used to show that the D1-D5 geometries do indeed correspond to R vacua with all the requisite properties.