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Journal Article

Conformal field theory complexity from Euler-Arnold equations


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

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Flory, M., & Heller, M. P. (2020). Conformal field theory complexity from Euler-Arnold equations. Journal of High Energy Physics, 2020(12): 91. doi:10.1007/JHEP12(2020)091.

Cite as: http://hdl.handle.net/21.11116/0000-0006-D486-3
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.