Complexity change under conformal transformations in AdS$_{3}$/CFT$_{2}$
Abstract
Using the volume proposal, we compute the change of complexity of holographic states caused by a small conformal transformation in AdS/CFT. 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.
Cite
@article{arxiv.1806.08376,
title = {Complexity change under conformal transformations in AdS$_{3}$/CFT$_{2}$},
author = {Mario Flory and Nina Miekley},
journal= {arXiv preprint arXiv:1806.08376},
year = {2019}
}
Comments
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