Alladi Ramakrishnan Hall

Information theoretic quantities from gauge/gravity correspondence

Sunandan Gangopadhyay

S. N. Bose National Centre for Basic Sciences, Kolkata

It has been realized in the last decade that information
theoretic quantities can be computed from the gauge/gravity
correspondence. A holographic formula for the entanglement entropy of a
subsystem in a d-dimensional conformal field theory living at the boundary
of the classical bulk theory has been proposed. In this context, we study
the flow of holographic entanglement entropy in dimensions d>=3. It is
observed that a generalized entanglement temperature T_g can be defined
which gives the Hawking temperature in the infrared region and leads to a
generalized thermodynamics like law E=[(d-1)/d]T_g S_{REE}, where S_{REE}
is the renormalized holographic entanglement entropy. Furthermore, in the
IR limit, T_g produces the Hawking temperature along with some correction
terms. The IR limit of S_{REE} gives the thermal entropy of the black hole
as the leading term, however, does not have a logarithmic correction
unlike the BTZ black hole. We also compute the exact form of the bulk
geometry from a 1+1-dimensional conformal field theory using the
holographic principle. The results show the influence of the boundary
ultra-violet cutoff on the bulk metric.

---------------------------------------------------------------------

The work is based on the following papers :

Phys. Rev. D 100 (2019) 106008

Eur. Phys. J. Plus 135 (2020) 132

----------------------------------------------------------------------