Deformed WZW models and Hodge theory. Part I

Thomas Grimm (Institute for Theoretical Physics, Utrecht University, Princetonplein 5, Utrecht, CC, 3584, The Netherlands) ; Jeroen Monnee (Institute for Theoretical Physics, Utrecht University, Princetonplein 5, Utrecht, CC, 3584, The Netherlands)

We investigate a relationship between a particular class of two-dimensional integrable non-linear σ-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the λ-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 σ-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.

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      "value": "We investigate a relationship between a particular class of two-dimensional integrable non-linear \u03c3-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the \u03bb-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 \u03c3-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."
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Published on:
16 May 2022
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2022 (2022)
Issue 5
Pages 1-34
DOI:
https://doi.org/10.1007/JHEP05(2022)103
arXiv:
2112.00031
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: