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Journal Article

Geometry of complexity in conformal field theory

MPS-Authors
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Heller,  Michal P.
Gravity, Quantum Fields and Information, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

2005.02415.pdf
(Preprint), 356KB

2005.02415_v3.pdf
(Preprint), 506KB

PhysRevResearch.2.043438.pdf
(Publisher version), 311KB

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Citation

Flory, M., & Heller, M. P. (2020). Geometry of complexity in conformal field theory. Physical Review Research, 2(4): 043438. doi:10.1103/PhysRevResearch.2.043438.


Cite as: http://hdl.handle.net/21.11116/0000-0006-84C4-7
Abstract
We study circuit and state complexity in the universal setting of (1+1)-dimensional conformal field theory and unitary transformations generated by the stress-energy tensor. We provide a unified view of assigning a cost to circuits based on the Fubini-Study metric and via direct counting of the stress-energy tensor insertions. In the former case, we iteratively solve the emerging integro-differential equation for sample optimal circuits and discuss the sectional curvature of the underlying geometry. In the latter case, we recognize that optimal circuits are governed by Euler-Arnold type equations and discuss relevant results for three well-known equations of this type in the context of complexity.