Actas de congresos
Rényi and Entanglement Entropies: some holographically calculable contributions
Fecha
2012Institución
Resumen
Entanglement is one of the most peculiar features of quantum systems.
In general, it is difficult to extract unambiguous, cut-off independent contributions
to its associated entropy. However, in the very special case of
conformally invariant fields and spherical entangling surfaces, a logarithmic
(in the cutoff) term can be identified whose universal coefficient is dictated
by type-A trace anomaly. In this contribution we present two alternative
derivations of this remarkably entropy-anomaly connection. Both start with
a conformal mapping to thermal entropy in a certain hyperbolic geometry.
One derivation considers this geometry as the near-horizon region of an extremal
black hole and the log-correction is computed, following Wald, as
Noether charge at the horizon. The second approach, in turn, contemplates
the hyperbolic geometry as the conformal boundary of a bulk hyperbolic
background; the AdS/CFT dictionary trades the boundary thermal entropy
for the functional determinant (one-loop effective action) of a dual bulk field.
The log-term shows up now as consequence of the holographic (or volume)
anomaly in the bulk. Finally, we show that the associated Rényi entropy can
be accounted for by a suitable q-deformation of the previous calculations.