Conformal field theory complexity from Euler-Arnold equations

Abstract

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.

A preprint version of the article is available at ArXiv.

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ArXiv ePrint: 2007.11555

On leave from: National Centre for Nuclear Research, Pasteura 7, 02-093 Warsaw, Poland (Michal P. Heller).

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Flory, M., Heller, M.P. Conformal field theory complexity from Euler-Arnold equations. J. High Energ. Phys. 2020, 91 (2020). https://doi.org/10.1007/JHEP12(2020)091

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Keywords

  • AdS-CFT Correspondence
  • Conformal Field Theory
  • Gauge-gravity correspondence