Deformed WZW Models and Hodge Theory -- Part I

DOI10.1007/JHEP05(2022)103arXiv2112.00031MaRDI QIDQ6384430

Jeroen Monnee, Thomas W. Grimm

Publication date: 30 November 2021

Abstract: We investigate a relationship between a particular class of two-dimensional integrable non-linear $sigma$-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the $lambda$-deformed $G/G$ model and show that a special class of solutions to its equations of motion precisely describes a one-parameter variation of Hodge structures. We find that this special class is obtained by identifying the group-valued field of the $sigma$-model with the Weil operator of the Hodge structure. In this way, the study of strings on classifying spaces of Hodge structures suggests an interesting connection between the broad field of integrable models and the mathematical study of period mappings.

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Supersymmetric field theories in quantum mechanics (81T60) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Topological field theories in quantum mechanics (81T45) Groups and algebras in quantum theory and relations with integrable systems (81R12) Period matrices, variation of Hodge structure; degenerations (32G20) Variation of Hodge structures (algebro-geometric aspects) (14D07)

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