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

TL;DR

This paper investigates how small conformal transformations affect the complexity of holographic states in AdS$_{3}$/CFT$_{2}$, providing a perturbative analysis that bridges holographic and field-theoretic complexity measures.

Contribution

It offers a second-order perturbative calculation of complexity change under conformal transformations in AdS$_{3}$/CFT$_{2}$ and compares holographic results with field-theoretic proposals.

Findings

Complexity change is computed perturbatively to second order.

Results enable comparison between holographic and field-theoretic complexity measures.

Explicit CFT operators generating conformal transformations are constructed.

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.