Homotopy Manin theories: generalising third-way, Yang–Mills and integrable sigma models

Alex S Arvanitakis; Leron Borsten; Dimitri Kanakaris; Hyungrok Kim

doi:10.1088/1751-8121/adfc17

Homotopy Manin theories: generalising third-way, Yang–Mills and integrable sigma models

Alex S Arvanitakis, Leron Borsten, Dimitri Kanakaris, Hyungrok Kim

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Abstract

Manin theories are a class of non-topological deformations of Chern–Simons theories that naturally realise the third-way mechanism and furthermore admit localisation despite not being supersymmetric in the usual sense. In this paper, we extend this construction to higher dimensions, thereby producing a large class of examples of third-way-type theories. Furthermore, the construction naturally yields Yang–Baxter integrable deformations of the principal chiral model as well as gravitational models various dimensions.

Original language	English
Article number	355401
Number of pages	21
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	58
Issue number	35
Early online date	27 Aug 2025
DOIs	https://doi.org/10.1088/1751-8121/adfc17
Publication status	Published - 1 Sept 2025

Keywords

integrable sigma model
Manin pair
AKSZ model
third-way theory

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10.1088/1751-8121/adfc17Licence: CC BY

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© 2025 The Author(s). This is an open access article distributed under the Creative Commons Attribution License, to view a copy of the license, see: https://creativecommons.org/licenses/by/4.0/.
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AU - Kim, Hyungrok

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AB - Manin theories are a class of non-topological deformations of Chern–Simons theories that naturally realise the third-way mechanism and furthermore admit localisation despite not being supersymmetric in the usual sense. In this paper, we extend this construction to higher dimensions, thereby producing a large class of examples of third-way-type theories. Furthermore, the construction naturally yields Yang–Baxter integrable deformations of the principal chiral model as well as gravitational models various dimensions.

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KW - AKSZ model

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JO - Journal of Physics A: Mathematical and Theoretical

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ER -

Homotopy Manin theories: generalising third-way, Yang–Mills and integrable sigma models

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