Horizons, holography and condensed matter

Abstract

The holographic correspondence creates an interface between classical gravitational physics and the dynamics of strongly interacting quantum field theories. This chapter will relate the physics of charged, asymptotically Anti-de Sitter spacetimes to the phenomenology of low temperature critical phases of condensed matter. Common essential features will characterise both the gravitational and field theoretic systems. Firstly, an emergent scaling symmetry at the lowest energy scales appears as an emergent isometry in the interior, `near horizon' regime of the spacetime. Secondly, the field theoretic distinction between fractionalized and mesonic phases appears as the presence or absence of a charge-carrying horizon in the spacetime. A perspective grounded in these two characteristics allows a unified presentation of `holographic superconductors', `electron stars' and `charged dilatonic spacetimes'.

Figures (7)

• Figure 1: The extra radial dimension in holography corresponds to the renormalisation group scale. Processes in the interior determine long distance physics, the IR, of the dual field theory while processes near the boundary control the short distance, or UV, physics.
• Figure 2: One loop correction to the boson propagator from fermions.
• Figure 3: The basic question in finite density holography: use the gravitational equations to motion to find the interior IR geometry given the boundary condition that there is an electric flux at infinity.
• Figure 4: The planar Reissner-Nordström-AdS black hole. The charge density is sourced entirely by flux emanating from the black hole horizon.
• Figure 5: The onset of the superconducting instability. Pair produced waves are repelled or attracted to the black hole depending on their charge.