Lifshitz Spacetime as a Window into Condensed Matter Physics.

We study applications of the AdS/CFT correspondence to strongly coupled condensed matter theories. Specifically, we focus on Lifshitz spacetime, which was proposed as a gravity dual to field theories with Lifshitz scaling symmetry. We first show that higher derivative corrections, such as those arising from string theory, can resolve the apparent tidal singularity of pure Lifshitz spacetime in the deep infrared. We do so by explicitly constructing a toy-model of 4-derivative gravity coupled to Maxwell-dilaton theory to show that the singular horizon can be resolved into a nonsingular AdS2xR2 geometry. Next, we demonstrate that the non-relativistic Lifshitz symmetry leads to an effective tunneling barrier for matter fields propagating in Lifshitz spacetime. In particular, the tunneling barrier causes scalar modes to either grow or decay exponentially near the boundary. We investigate two consequences of this behavior: First, we show that the boundary-to-bulk correlator, or smearing function, is not well-defined in Lifshitz spacetime, due to a divergence at large momenta and small frequencies. Second, we show that the boundary retarded Green's function for scalar operators is insensitive to small changes in the near-horizon geometry. This insensitivity manifests itself in an exponentially small spectral function at low energies and large momenta. We show that this exponential behavior of the spectral weight is robust with respect to higher derivative corrections in the bulk, and is therefore a concrete prediction of AdS/CFT for condensed matter systems. We conclude by giving a field theory interpretation of the exponential behavior in terms of a non-perturbative resummation of Feynman diagrams.PhDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120658/1/gknodel_1.pd

Hidden horizons in non-relativistic AdS/CFT

We study boundary Green's functions for spacetimes with non-relativistic scaling symmetry. For this class of backgrounds, scalar modes with large transverse momentum, or equivalently low frequency, have an exponentially suppressed imprint on the boundary. We investigate the effect of these modes on holographic two-point functions. We find that the boundary Green's function is generically insensitive to horizon features on small transverse length scales. We explicitly demonstrate this insensitivity for Lifshitz z=2, and then use the WKB approximation to generalize our findings to Lifshitz z>1 and RG flows with a Lifshitz-like region. We also comment on the analogous situation in Schroedinger spacetimes. Finally, we exhibit the analytic properties of the Green's function in these spacetimes.Comment: Abstract and Introduction updated, typos correcte

Universal features of Lifshitz Green's functions from holography

We examine the behavior of the retarded Green's function in theories with Lifshitz scaling symmetry, both through dual gravitational models and a direct field theory approach. In contrast with the case of a relativistic CFT, where the Green's function is fixed (up to normalization) by symmetry, the generic Lifshitz Green's function can a priori depend on an arbitrary function $\mathcal G(\hat\omega)$, where $\hat\omega=\omega/|\vec k|^z$ is the scale-invariant ratio of frequency to wavenumber, with dynamical exponent $z$. Nevertheless, we demonstrate that the imaginary part of the retarded Green's function (i.e. the spectral function) of scalar operators is exponentially suppressed in a window of frequencies near zero. This behavior is universal in all Lifshitz theories without additional constraining symmetries. On the gravity side, this result is robust against higher derivative corrections, while on the field theory side we present two $z=2$ examples where the exponential suppression arises from summing the perturbative expansion to infinite order.Comment: 32 pages, 4 figures, v2: reference added, v3: fixed bug in bibliograph