Q-curvature and Path Integral Complexity

Understand

We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions.

• This perspective allows for a systematical construction of the higher-dimensional path integral complexity in holographic conformal field theories in terms of Q-curvature actions.
• We explore the properties and consequences of these actions from the perspective of the optimization programme, tensor networks and penalty factors.
• Moreover, in the context of recently proposed holographic path integral optimization, we consider higher curvature contributions on the Hartle-Hawking bulk slice and study their impact on the optimization as well as their relation to Q-curvature actions and finite cut-off holography.