Abstract
We develop basic tools and matching conditions to interpolate between asymptotic and near horizon symmetries. We focus on black holes in three dimensions. In particular, we match Brown-Henneaux boundary conditions at infinity, which yields two Virasoro algebras, to Heisenberg boundary conditions at the horizon yielding two û(1) current algebras. Our construction allows to equip BTZ black holes with soft hair excitations at the horizon invisible to the asymptotic observer.
Highlights
Not recover the appropriate set of symmetries
We develop basic tools and matching conditions to interpolate between asymptotic and near horizon symmetries
Introducing a finite cutoff at both boundaries renders the cutoff surfaces timelike in most applications, so that we are in a situation where we have two disconnected boundary components, e.g. one at a radial distance close to the black hole horizon and the other one close to the asymptotic boundary
Summary
We recall salient features of Chern-Simons theories, without yet emphasizing their specific gravitational role. The equations of motion (2.2) imply gauge flatness of the connection,. Where g is some group element of the underlying gauge group This means there are no local physical degrees of freedom in the Chern-Simons theory; it is a topological quantum field theory of Schwartz type [28]. Systems described by Chern-Simons theories on manifolds with boundaries can have physical degrees of freedom, often referred to as “edge-states” in quantum Hall contexts Boundary conditions on the gauge connection A are a crucial physical input in the theory. Different choices are possible and can lead to different physical phase spaces and symmetry algebras acting on them, see [30] for a summary of possibilities in three-dimensional Einstein gravity with negative cosmological constant. We consider Chern-Simons theories on manifolds with two boundaries
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