Integrability structures in string theory

K.A. Gubarev^†^a, b, E.T. Musaev^‡^a
^aMoscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation
^bNational Research Centre ‘Kurchatov Institute’, pl. akad. Kurchatova 1, Moscow, 123182, Russian Federation

This review is a collection of various methods and observations relevant to structures in three-dimensional systems similar to those responsible for the integrability of two-dimensional systems. Particular focus is on Nambu structures and loop variables naturally appearing in membrane dynamics. While reviewing each topic in more detail, we emphasize connections among them and speculate on possible relations to membrane integrability.

Keywords: integrability, Nambu structure, loop algebra, membranes, M-theory
PACS: 02.30.Ik, 04.65.+e, 11.25.−w (all)
DOI: 10.3367/UFNe.2023.06.039407
URL: https://ufn.ru/en/articles/2024/3/a/
Citation: Gubarev K A, Musaev E T "Integrability structures in string theory" Phys. Usp. 67 219–250 (2024)

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Received: 20th, January 2023, revised: 7th, June 2023, accepted: 17th, June 2023

Оригинал: Губарев К А, Мусаев Э Т «Интегрируемые структуры в теории струн» УФН 194 233–267 (2024); DOI: 10.3367/UFNr.2023.06.039407