Complexity for Conformal Field Theories in General Dimensions

Nicolas Chagnet, Shira Chapman, Jan de Boer, Claire Zukowski

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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.

Original languageEnglish
Article number051601
JournalPhysical Review Letters
Volume128
Issue number5
DOIs
StatePublished - 31 Jan 2022

ASJC Scopus subject areas

  • General Physics and Astronomy

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