String Theory Journal Club

In this talk I will describe circuit complexity for conformal field theories in arbitrary dimensions. I will consider gates built from a unitary representation of the Lorentzian conformal group, two different circuit cost functions, and paths that start from an initial primary state. The results can be understood in terms of the geometry of coadjoint orbits of the conformal group. I will also explain how these methods can be extended to study circuits in other symmetry groups using a group theoretic generalization of the notion of coherent states. Finally, I will describe a connection to timelike geodesics in anti-de Sitter spacetimes.