What Spatial Geometries do (2+1)-Dimensional Quantum Field Theory Vacua Prefer?

We consider relativistic (2+1)-dimensional quantum field theories (QFTs) on a product of time with a two-space and study the vacuum free energy as a functional of the temperature and spatial geometry. We focus on free scalar and Dirac fields on arbitrary perturbations of flat space, finding that the free energy difference from flat space is finite and always negative to leading order in the perturbation. Thus, free (2+1)-dimensional QFTs appear to always energetically favor a crumpled space on all scales; this is true both as a purely quantum effect at zero temperature and as a purely thermal effect at high temperature. Importantly, we show that this quantum effect is non-negligible for the relativistic Dirac degrees of freedom on monolayer graphene even at room temperature, so we argue that this vacuum energy effect should be included for a proper analysis of the equilibrium configuration of graphene or similar materials.

Stationary holographic plasma quenches and numerical methods for non-killing horizons.

We explore use of the harmonic Einstein equations to numerically find stationary black holes where the problem is posed on an ingoing slice that extends into the interior of the black hole. Requiring no boundary conditions at the horizon beyond smoothness of the metric, this method may be applied for horizons that are not Killing. As a nontrivial illustration we find black holes which, via AdS-CFT, describe a time-independent CFT plasma flowing through a static spacetime which asymptotes to Minkowski in the flow's past and future, with a varying spatial geometry in between. These are the first nonperturbative examples of stationary black holes which do not have Killing horizons. When the CFT spacetime slowly varies, the CFT stress tensor derived from gravity is well described by viscous hydrodynamics. For fast variation it is not, and the solutions are stationary analogs of dynamical quenches, with the plasma being suddenly driven out of equilibrium. We find evidence these flows become unstable for sufficiently strong quenches, and speculate the instability may be turbulent.

Gravity and large black holes in Randall-Sundrum II braneworlds.

We show how to construct low energy solutions to the Randall-Sundrum II (RSII) model by using an associated five-dimensional anti-de Sitter space (AdS(5)) and/or four-dimensional conformal field theory (CFT(4)) problem. The RSII solution is given as a perturbation of the AdS(5)-CFT(4) solution, with the perturbation parameter being the radius of curvature of the brane metric compared to the AdS length ℓ. The brane metric is then a specific perturbation of the AdS(5)-CFT(4) boundary metric. For low curvatures the RSII solution reproduces 4D general relativity on the brane. Recently, AdS(5)-CFT(4) solutions with a 4D Schwarzschild boundary metric were numerically constructed. We modify the boundary conditions to numerically construct large RSII static black holes with radius up to ~20ℓ. For a large radius, the RSII solutions are indeed close to the associated AdS(5)-CFT(4) solution.

Holographic superconductivity in M theory.

Using seven-dimensional Sasaki-Einstein spaces we construct solutions of D=11 supergravity that are holographically dual to superconductors in three spacetime dimensions. Our numerical results indicate a new zero temperature solution dual to a quantum critical point.

Connecting black holes and black strings.

Static vacuum spacetimes with one compact dimension include black holes with localized horizons but also uniform and nonuniform black strings where the horizon wraps over the compact dimension. We present new numerical solutions for these localized black holes in 5 and 6 dimensions. Combined with previous 6D nonuniform string results, these provide evidence that the black hole and nonuniform string branches join at a topology changing solution.