Lecturer: Dr. Justin David
Affiliation: Centre for High Energy Physics,
Indian Institute of Science
Abstract:
We derive a spectral sum rule in the
shear channel for conformal field theories
in general d> 2 dimensions held at finite
temperature. The sum rule result from
the OPE of the stress tensor at high
frequency as well as the hydrodynamic
behavior of the theory at low
frequencies. The sum rule states that a
weighted integral of the spectral density
over frequencies is proportional to the
energy density of the theory. We show
that the proportionality constant can be
written in terms the Maldacena-Hofman
variables t_2, t_4 which rely on data
which determines the three point function
of the stress tensor of the CFT. For
theories which admit a two derivative
gravity dual this proportionality constant
is given by d/2(d+1) . We then use
causality constraints and obtain bounds
on the sum rule which are valid for any
conformal field theory. We illustrate the
sum rule by applying it to well studied
conformal field theories in d=3, 4, 6.
dimensions.
Additional details of the upcoming Joint
Seminars in Theoretical High Energy Physics
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