@article{fd027ed31fcb45b2b02bdcb197009e0d,
title = "Complexity for Conformal Field Theories in General Dimensions",
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.",
author = "Nicolas Chagnet and Shira Chapman and {de Boer}, Jan and Claire Zukowski",
note = "Funding Information: We would like to thank Igal Arav, Costas Bachas, Ning Bao, Alexandre Belin, Adam Chapman, Bartlomiej Czech, Lorenzo Di Pietro, Ben Freivogel, Vladimir Gritsev, Austin Joyce, Kurt Hinterbichler, Marco Meineri, Yaron Oz, Giuseppe Policastro, and Jan Zaanen for valuable comments and discussions. We are particularly grateful to Bartlomiej Czech for suggesting to look for a relation between the FS metric and minimal and maximal distances between timelike geodesics. The work of N. C. is supported in part by the Dutch Research Council (NWO project 680.91.116), and by the Dutch Research Council/Ministry of Science and Education (NWO/OCW)/Delta Institute for Theoretical Physics. The work of S. C. is supported by the Israel Science Foundation (Grant No. 1417/21). S. C. also acknowledges the support of Carole and Marcus Weinstein through the BGU Presidential Faculty Recruitment Fund. The work of J. d. B is supported by the European Research Council under the European Union{\textquoteright}s Seventh Framework Programme (FP7/2007-2013), ERC Grant agreement ADG 834878. C. Z. is supported by the ERC Consolidator Grant QUANTIVIOL. Publisher Copyright: {\textcopyright} 2022 American Physical Society",
year = "2022",
month = jan,
day = "31",
doi = "10.1103/PhysRevLett.128.051601",
language = "English",
volume = "128",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "5",
}