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Instantons, renormalons and the theta angle in integrable sigma models

by Marcos Marino, Ramon Miravitllas, Tomas Reis

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Submission summary

Authors (as registered SciPost users): Marcos Mariño · Ramon Miravitllas · Tomas Reis
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-09-27
Date submitted: 2023-08-28 11:40
Submitted by: Reis, Tomas
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • High-Energy Physics - Phenomenology
  • Mathematical Physics
Approach: Theoretical


Some sigma models which admit a theta angle are integrable at both $\vartheta=0$ and $\vartheta=\pi$. This includes the well-known $O(3)$ sigma model and two families of coset sigma models studied by Fendley. We consider the ground state energy of these models in the presence of a magnetic field, which can be computed with the Bethe ansatz. We obtain explicit results for its non-perturbative corrections and we study the effect of the theta angle on them. We show that imaginary, exponentially small corrections due to renormalons remain unchanged, while instanton corrections change sign, as expected. We find in addition corrections due to renormalons which also change sign as we turn on the theta angle. Based on these results we present an explicit non-perturbative formula for the topological susceptibility of the $O(3)$ sigma model in the presence of a magnetic field, in the weak coupling limit.

List of changes

1) We clarified the discussion of the deformed "sausage" models to better explain why there are no renormalons in such models. This affects the relevant paragraph in section 1.

2) We added details to the discussion of the non-perturbative effects in the coset sigma models to clarify why some are classified as instantons and other as renormalons, as well as the implications of such distinction. This affects the end of section 4.2 and a little bit of section 5.

3) We updated the references to the convention where Alexei Zamolodchikov is referred as Al. B. Zamolodchikov while Alexander Zamolodchikov is referred as A. B. Zamolodchikov.

Published as SciPost Phys. 15, 184 (2023)

Reports on this Submission

Anonymous Report 2 on 2023-9-25 (Invited Report)


The authors have scantly addressed the comments/questions I raised. I can however recommend publication in SciPost.

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Anonymous Report 1 on 2023-9-10 (Invited Report)


The authors addressed my comments in my first report, and so I recommend publication in SciPost in this form.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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