Abstract
We study circuit complexity for conformal field theory states in an arbitrary number of dimensions. Our circuits start from a primary state and move along a unitary representation of the Lorentzian conformal group. Different choices of distance functions can be understood in terms of the geometry of coadjoint orbits of the conformal group. We explicitly relate our circuits to timelike geodesics in anti-de Sitter space and the complexity metric to distances between these geodesics. We extend our method to circuits in other symmetry groups using a group theoretic generalization of the notion of coherent states.
Highlights
We study circuit complexity for conformal field theory states in an arbitrary number of dimensions
Our circuits live in a phase space that is a coadjoint orbit of the conformal group and the various cost functions take the form of simple geometric notions on these orbits
III, we present the result for the complexity of conformal field theories (CFTs) states in general dimensions
Summary
We study circuit complexity for conformal field theory states in an arbitrary number of dimensions. Our circuits start from a primary state and move along a unitary representation of the Lorentzian conformal group. Different choices of distance functions can be understood in terms of the geometry of coadjoint orbits of the conformal group.
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