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SUMMARY: Constraining spectral densities in conformal field theories (Quan
tum Spacetime Seminar series)
DTSTART;VALUE=DATE-TIME:20180212T060000Z
DTEND;VALUE=DATE-TIME:20180212T070000Z
DTSTAMP;VALUE=DATE-TIME:20190220T045804Z
UID:indico-event-6223@cern.ch
DESCRIPTION:We derive constraints on spectral density of the shear correla
tors of conformal field theories at finite temperature in general d > 3 di
mensions. The resulting sum rules are due to conformal invariance and low
energy hydrodynamic behaviour. The sum rule states that a weighted integra
l of the spectral density over frequencies is proportional to the energy d
ensity of the theory. We show that the proportionality constant can be wri
tten in terms of the Hofman-Maldacena variables t2\, t4 which determine th
e three point function of the stress tensor. For theories which admit a tw
o derivative gravity dual this proportionality constant is given by d/(2(d
+1)). We also compute corrections to the holographic shear sum rule in pre
sence of higher derivative corrections to the Einstein-Hilbert action. We
find agreement between the sum rule obtained from a general CFT analysis a
nd holographic computation. We then use causality constraints and obtain b
ounds on the sum rule which are valid in any conformal field theory. Final
ly we demonstrate that the high frequency behavior of the spectral functio
n in the vector and the tensor channel are also determined by the Hofman-M
aldacena variables.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay
.py?confId=6223
LOCATION: A304
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6223
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