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Conformal field theory complexity from Euler-Arnold equations

Defining complexity in quantum field theory is a difficult task, and the main challenge concerns going beyond free models and associated Gaussian states and operations. One take on this issue is to consider conformal field theories in 1+1 dimensions and our work is a comprehensive study of state and...

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Autores principales: Flory, Mario, Heller, Michal P.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7737416/
https://www.ncbi.nlm.nih.gov/pubmed/33343184
http://dx.doi.org/10.1007/JHEP12(2020)091
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author Flory, Mario
Heller, Michal P.
author_facet Flory, Mario
Heller, Michal P.
author_sort Flory, Mario
collection PubMed
description Defining complexity in quantum field theory is a difficult task, and the main challenge concerns going beyond free models and associated Gaussian states and operations. One take on this issue is to consider conformal field theories in 1+1 dimensions and our work is a comprehensive study of state and operator complexity in the universal sector of their energy-momentum tensor. The unifying conceptual ideas are Euler-Arnold equations and their integro-differential generalization, which guarantee well-posedness of the optimization problem between two generic states or transformations of interest. The present work provides an in-depth discussion of the results reported in arXiv:2005.02415 and techniques used in their derivation. Among the most important topics we cover are usage of differential regularization, solution of the integro-differential equation describing Fubini-Study state complexity and probing the underlying geometry.
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spelling pubmed-77374162020-12-15 Conformal field theory complexity from Euler-Arnold equations Flory, Mario Heller, Michal P. J High Energy Phys Regular Article - Theoretical Physics Defining complexity in quantum field theory is a difficult task, and the main challenge concerns going beyond free models and associated Gaussian states and operations. One take on this issue is to consider conformal field theories in 1+1 dimensions and our work is a comprehensive study of state and operator complexity in the universal sector of their energy-momentum tensor. The unifying conceptual ideas are Euler-Arnold equations and their integro-differential generalization, which guarantee well-posedness of the optimization problem between two generic states or transformations of interest. The present work provides an in-depth discussion of the results reported in arXiv:2005.02415 and techniques used in their derivation. Among the most important topics we cover are usage of differential regularization, solution of the integro-differential equation describing Fubini-Study state complexity and probing the underlying geometry. Springer Berlin Heidelberg 2020-12-15 2020 /pmc/articles/PMC7737416/ /pubmed/33343184 http://dx.doi.org/10.1007/JHEP12(2020)091 Text en © The Author(s) 2020 Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0 (http://creativecommons.org/licenses/by/4.0/) ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
spellingShingle Regular Article - Theoretical Physics
Flory, Mario
Heller, Michal P.
Conformal field theory complexity from Euler-Arnold equations
title Conformal field theory complexity from Euler-Arnold equations
title_full Conformal field theory complexity from Euler-Arnold equations
title_fullStr Conformal field theory complexity from Euler-Arnold equations
title_full_unstemmed Conformal field theory complexity from Euler-Arnold equations
title_short Conformal field theory complexity from Euler-Arnold equations
title_sort conformal field theory complexity from euler-arnold equations
topic Regular Article - Theoretical Physics
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7737416/
https://www.ncbi.nlm.nih.gov/pubmed/33343184
http://dx.doi.org/10.1007/JHEP12(2020)091
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