Geometry and Complexity of Path Integrals in Inhomogeneous CFTs

Understand

In this work we develop the path integral optimization in a class of inhomogeneous 2d CFTs constructed by putting an ordinary CFT on a space with a position dependent metric.

• After setting up and solving the general optimization problem, we study specific examples, including the M\"obius, SSD and Rainbow deformed CFTs, and analyze path integral geometries and complexity for universal classes of states in these models.
• We find that metrics for optimal path integrals coincide with particular slices of $AdS_3$ geometries, on which Einstein's equations are equivalent to the condition for minimal path integral complexity.
• We also find that while leading divergences of path integral complexity remain unchanged, constant contributions are modified in a universal, position dependent manner.