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arXiv · 2004.11377

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

Bowen Chen·Bartlomiej Czech·Zi-zhi Wang
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Abstract

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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Bowen Chen, Bartlomiej Czech, Zi-zhi Wang. 2020-04-23. Cutoff Dependence and Complexity of the CFT$_2$ Ground State. https://doi.org/10.1103/physrevd.103.026015

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