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TMF, 2021, Volume 208, Number 2, Pages 165–179 (Mi tmf10103)  

Sigma models as Gross–Neveu models

D. V. Bykov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We review the correspondence between integrable sigma models with complex homogeneous target spaces and the chiral bosonic (and possibly mixed bosonic/fermionic) Gross–Neveu models. Mathematically, these are models with quiver variety phase spaces, which reduce to more conventional sigma models in special cases. We discuss the geometry of the models as well as their trigonometric and elliptic deformations, the Ricci flow, and the inclusion of fermions.

Keywords: sigma model, integrable model, Gross–Neveu model, quiver variety, Ricci flow.

Funding Agency Grant Number
Russian Science Foundation 20-72-10144
This work was supported by the Russian Science Foundation grant RSCF-20-72-10144.


DOI: https://doi.org/10.4213/tmf10103

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English version:
Theoretical and Mathematical Physics, 2021, 208:2, 993–1003

Bibliographic databases:

Received: 31.03.2021
Revised: 31.03.2021

Citation: D. V. Bykov, “Sigma models as Gross–Neveu models”, TMF, 208:2 (2021), 165–179; Theoret. and Math. Phys., 208:2 (2021), 993–1003

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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