SMuK 2021 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 1: AdS-CFT I

MP 1.2: Talk

Monday, August 30, 2021, 11:25–11:50, H3

Realizing Computational Complexity in Conformal Field Theory — Johanna Erdmenger, Marius Gerbershagen, and •Anna-Lena Weigel — Julius-Maximilians-Universität Würzburg, 97074 Würzburg, Germany

An important question for the AdS/CFT correspondence is how the bulk geometry is encoded in the boundary field theory. A useful quantity proposed in this context is computational complexity. This is a concept adapted from quantum information that counts the minimum number of simple steps, gates, necessary to perform a calculation. While there exist concrete proposals for complexity in the AdS gravity theory, it remains an open question how to define it in a CFT. To make progress in this direction, a recent proposal suggests to restrict the allowed set of gates to symmetry transformations. This was employed to compute complexity for conformal transformations in 2d CFTs [1]. We generalize this approach to Kac-Moody symmetries and show that the complexity is equal to actions defined on coadjoint orbits of the according symmetry group. In this way, we calculate the complexity for several examples of CFTs [2]. The coadjoint orbit actions also arise from 3d gravity theory. We comment on connections between these gravity actions and complexity.

[1] P. Caputa, J. Magan. "Quantum Computation as Gravity". In: Phys. Rev. Lett. 122 (2019), p. 231302. arXiv:1807.04422 [hep-th].

[2] J. Erdmenger, M. Gerbershagen, A. Weigel. "Complexity measures from geometric actions on Virasoro and Kac-Moody orbits". In: JHEP 11 (2020) 003. arXiv:2004.03619 [hep-th].