TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.5.184
TI  - Instantons, renormalons and the theta angle in integrable sigma models
PY  - 2023/11/03
UR  - https://scipost.org/SciPostPhys.15.5.184
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 5
SP  - 184
A1  - Mariño, Marcos
AU  - Miravitllas, Ramon
AU  - Reis, Tomás
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.15.5.184,
	title={{Instantons, renormalons and the theta angle in integrable sigma models}},
	author={Marcos Mariño and Ramon Miravitllas and Tomas Reis},
	journal={SciPost Phys.},
	volume={15},
	pages={184},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.5.184},
	url={https://scipost.org/10.21468/SciPostPhys.15.5.184},
}