WdW-patches in $AdS_{3}$ and complexity change under conformal transformations II

doi:10.1007/JHEP05(2019)086

WdW-patches in $AdS_{3}$ and complexity change under conformal transformations II

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WdW-patches in $AdS_{3}$ and complexity change under conformal transformations II

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punktacja MEiN [2019]: 140

title:	WdW-patches in $AdS_{3}$ and complexity change under conformal transformations II
author:	Flory Mario
journal title:	The Journal of High Energy Physics
volume:	2019
issue:	5
date of publication :	2019
article ID:	86
ISSN:	1126-6708
eISSN:	1029-8479
DOI:	10.1007/JHEP05(2019)086
language:	English
journal language:	English
abstract in English:	We study the null-boundaries of Wheeler-de Witt (WdW) patches in three dimensional Poincaré-AdS, when the selected boundary timeslice is an arbitrary (non-constant) function, presenting some useful analytic statements about them. Special attention will be given to the piecewise smooth nature of the null-boundaries, due to the emergence of caustics and null-null joint curves. This is then applied, in the spirit of one of our previous papers, to the problem of how the complexity of the CFT2 groundstate changes under a small local conformal transformation according to the action (CA) proposal. In stark contrast to the volume (CV) proposal, where this change is only proportional to the second order in the infinitesimal expansion parameter $\sigma$, we show that in the CA case we obtain terms of order $\sigma$ and even $\sigma log(\sigma )$. This has strong implications for the possible field-theory duals of the CA proposal, ruling out an entire class of them.
keywords in English:	AdS-CFT correspondence, gauge-gravity correspondence
affiliation:	Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
type:	journal article
subtype:	academic paper