标题： 瞬子、重整子和可积sigma模型中的theta角度 显示英文标题

标题： Instantons, renormalons and the theta angle in integrable sigma models

摘要： 一些允许存在θ角的σ模型在$\vartheta=0$和$\vartheta=\pi$处都是可积的。 这包括著名的$O(3)$σ 模型以及 Fendley 研究的两类 coset σ 模型。 我们考虑这些模型在磁场中的基态能量，可以用 Bethe 方程计算。 我们得到了非微扰修正的显式结果，并研究了θ角对其的影响。 我们证明了由于重整子引起的虚指数小校正保持不变，而瞬子校正改变符号，正如预期的那样。 此外，我们还发现了由于重整子引起的校正，当开启θ角时，这些校正的符号也会发生变化。 基于这些结果，我们在弱耦合极限下给出了磁场中$O(3)$σ 模型拓扑易感性的显式非微扰公式。 显示英文摘要

摘要： 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.