Resurgence and Dynamics of O(N) and Grassmannian Sigma Models

Understand

We study the non-perturbative dynamics of the two dimensional ${O(N)}$ and Grassmannian sigma models by using compactification with twisted boundary conditions on $\mathbb R \times S^1$, semi-classical techniques and resurgence.

• While the $O(N)$ model has no instantons for $N>3$, it has (non-instanton) saddles on $\mathbb R^2$, which we call 2d-saddles.
• On $\mathbb R \times S^1$, the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the ${\frak o}(N) $ algebra.
• These events may be viewed as fractionalizations of the 2d-saddles.