Complexity change under conformal transformations in AdS$_{3}$/CFT$_{2}$ - INSPIRE

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Complexity change under conformal transformations in AdS $_{3}$ /CFT $_{2}$

Mario Flory
(
- Jagiellonian U.
)
,
Nina Miekley
(
- Wurzburg U.
)

Jun 21, 2018

23 pages

Published in:

JHEP 05 (2019) 003

Published: May 2, 2019

e-Print:

1806.08376 [hep-th]

DOI:

10.1007/JHEP05(2019)003

View in:

reference search57 citations

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Abstract: (Springer)

Using the volume proposal, we compute the change of complexity of holographic states caused by a small conformal transformation in AdS

_{3}

/CF T

_{2}

. This computation is done perturbatively to second order. We give a general result and discuss some of its properties. As operators generating such conformal transformations can be explicitly constructed in CFT terms, these results allow for a comparison between holographic methods of defining and computing computational complexity and purely field-theoretic proposals. A comparison of our results to one such proposal is given.

Note:

v2: 23 pages, 5 figures, added references and one entirely new section about a comparison to a field theory proposal v3: 27 pages, 5 figures, minor improvements. Matches published version

AdS-CFT Correspondence
Gauge-gravity correspondence
transformation: conformal
field theory: conformal
anti-de Sitter
holography

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