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

Understand

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.