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

Mario Flory; Nina Miekley

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

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arxiv 1806.08376 v3 pith:IORJI7ZK submitted 2018-06-21 hep-th gr-qc

Mario Flory , Nina Miekley This is my paper · ORCID

classification hep-thgr-qc

keywords complexityconformalchangecomparisonholographicproposalresultstransformations

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abstract

Using the volume proposal, we compute the change of complexity of holographic states caused by a small conformal transformation in AdS$_{3}$/CFT$_{2}$. 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.

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