https://doi.org/10.1140/epjc/s10052-026-15534-1
Regular Article - Theoretical Physics
Three-loop singularity structure for a non-linear sigma model
1
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, 27 Fontanka, 191023, St. Petersburg, Russia
2
Saint Petersburg State University, 7/9 Universitetskaya Emb., 199034, St. Petersburg, Russia
3
National Research University Higher School of Economics, 6 Usacheva St., 119048, Moscow, Russia
a
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Received:
15
July
2025
Accepted:
8
March
2026
Published online:
6
May
2026
Abstract
The paper is devoted to the three-loop renormalization of the effective action for a two-dimensional non-linear sigma model using the background field method and a cutoff regularization in the coordinate representation. The coefficients of the renormalization constant and the necessary auxiliary vertices are found, as well as the asymptotic expansions of all three-loop diagrams, and their dependence on the type of regularizing function. A comparison is also made with the standard case of cutoff in the momentum representation.
On the 85-th anniversary of PDMI RAS.
© The Author(s) 2026
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