Reflections on Virasoro circuit complexity and Berry phase

Understand

Recently, the notion of circuit complexity defined in symmetry group manifolds has been related to geometric actions which generally arise in the coadjoint orbit method in representation theory and play an important role in geometric quantization.

• On the other hand, it is known that there exists a precise relation between geometric actions and Berry phases defined in group representations.
• Motivated by these connections, we elaborate on a relation between circuit complexity and the group theoretic Berry phase.
• As the simplest setup relevant for holography, we discuss the case of two dimensional conformal field theories.