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SUMMARY:The Crossed Product Construction from Holographic Quantum Error-Co
rrecting Codes
DTSTART;VALUE=DATE-TIME:20230316T053000Z
DTEND;VALUE=DATE-TIME:20230316T063000Z
DTSTAMP;VALUE=DATE-TIME:20231201T160620Z
UID:indico-event-8854@cern.ch
DESCRIPTION:Recently\, the old observation that the generalised entropy of
a horizon --- the sum of the area and the entropy of exterior fields ---
is better defined than either of the objects that make it up has been put
on firmer footing by Witten et al. The main observation is that including
fluctuations in the ADM charges in the algebra of matter fields changes th
e type of algebra from type III_1 --- which doesn't have an entropy functi
on --- to type II --- which does --- using the crossed product constructio
n. We show that a holographic quantum error-correcting (QEC) code naturall
y has a structure analogous to the crossed product. When the encoded algeb
ra is type I\, we show that ‘boundary modular flow’ in the code makes
it into a direct sum of type I factors. In the limit where we take the enc
oded algebra towards a type III_1 algebra\, a certain recasting of the dir
ect sum becomes a type II algebra. We are able to recover both type II_\\i
nfty --- relevant for black holes --- as well as type II_1 algebras -- rel
evant for cosmological horizons in de Sitter space --- by imposing differe
nt constraints on the area operator in the code. These results indicate th
at the holographic QEC code might be useful in contexts where the 'boundar
y' is actually an observer\, like the static patch of de Sitter.\n\nhttps:
//indico.tifr.res.in/indico/conferenceDisplay.py?confId=8854
LOCATION: A304 and on zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8854
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