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Cutoff Dependence and Complexity of the CFT$_2$ Ground State

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 نشر من قبل Bartlomiej Czech
 تاريخ النشر 2020
  مجال البحث
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We present the vacuum of a two-dimensional conformal field theory (CFT$_2$) as a network of Wilson lines in $SL(2,mathbb{R}) times SL(2,mathbb{R})$ Chern-Simons theory, which is conventionally used to study gravity in three-dimensional anti-de Sitter space (AdS$_3$). The position and shape of the network encode the cutoff scale at which the ground state density operator is defined. A general argument suggests identifying the `density of complexity of this network with the extrinsic curvature of the cutoff surface in AdS$_3$, which by the Gauss-Bonnet theorem agrees with the holographic Complexity = Volume proposal.



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