## Instantons, renormalons and the theta angle in integrable sigma models

Marcos Mariño, Ramon Miravitllas, Tomas Reis

SciPost Phys. 15, 184 (2023) · published 3 November 2023

- doi: 10.21468/SciPostPhys.15.5.184
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### Abstract

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.

### Cited by 3

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Marcos Mariño, -
^{1}Ramon Miravitllas, -
^{1}^{2}Tomás Reis

^{1}Université de Genève / University of Geneva [UNIGE]^{2}Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies [SISSA]

- European Research Council [ERC]
- Instituto Nazionale di Fisica Nucleare (INFN) (through Organization: Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN])
- Ministero dell'Università e della Ricerca