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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Berlin Heidelberg
2020
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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. |
format | Online Article Text |
id | pubmed-7737416 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
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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