Complexity for Conformal Field Theories in General Dimensions

• URL: http://arxiv.org/abs/2103.06920v2
• Date: Wed, 13 Oct 2021 18:02:39 GMT
• Title: Complexity for Conformal Field Theories in General Dimensions
• Authors: Nicolas Chagnet, Shira Chapman, Jan de Boer, Claire Zukowski
• Abstract summary: We study circuit complexity for conformal field theory states in arbitrary dimensions. Our circuits start from a primary state and move along a unitary representation of the Lorentzian conformal group.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study circuit complexity for conformal field theory states in arbitrary 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.

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