Peculiarities of beta functions in sigma models

Gamayun, Oleksandr; Losev, Andrei; Shifman, Mikhail

doi:10.1007/jhep10(2023)097

Title: Peculiarities of beta functions in sigma models

Journal Article · 17 October 2023 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep10(2023)097 · OSTI ID:2234293

Gamayun, Oleksandr ^[1]; Losev, Andrei ^[2]; Shifman, Mikhail ^[3]

London Institute for Mathematical Sciences (United Kingdom)
Chinese Academy of Sciences, Beijing (China); National Research University Higher School of Economics, Moscow (Russia)
University of Minnesota, Minneapolis, MN (United States)

In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to β functions and compare its results with the standard geometric calculations. Already in the second loop, we observe deviations from the geometric results that cannot be explained by the regularization/renormalization scheme choices. Moreover, in certain cases the first-order calculations produce results that are not symmetric under the classical diffeomorphisms of the target space. Although we could not present the full solution to this remarkable phenomenon, we found some indirect arguments indicating that an anomaly similar to that established in supersymmetric Yang-Mills theory might manifest itself starting from the second loop. We discuss why the difference between two answers might be an infrared effect, similar to that in β functions in supersymmetric Yang-Mills theories.

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Research Organization:: Univ. of Minnesota, Minneapolis, MN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011842

OSTI ID:: 2234293

Journal Information:: Journal of High Energy Physics (Online), Vol. 2023, Issue 10; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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