论文标题
instantons，renormalons和theta角度在可集成的西格玛模型中
Instantons, renormalons and the theta angle in integrable sigma models
论文作者
论文摘要
某些接纳theta角度的Sigma模型在$ \ vartheta = 0 $和$ \ vartheta =π$上都可以整合。这包括著名的$ O（3）$ Sigma模型和Fendley研究的两个Coset Sigma模型。我们考虑在存在磁场的情况下这些模型的基态能量，该磁场可以用bethe ansatz计算。我们为其非扰动校正获得了明确的结果，并研究了theta角对它们的影响。我们表明，由于预期的，由于肾结龙引起的假想，指数的小校正保持不变，而internon校正会更改符号。我们发现，由于雷诺马龙（Renormalons）的校正，这些校正也会在我们打开theta角时改变标志。基于这些结果，我们提出了一个明确的非扰动公式，用于在磁场存在下$ O（3）$ sigma模型在弱耦合极限下的拓扑敏感性。
Some sigma models which admit a theta angle are integrable at both $\vartheta=0$ and $\vartheta=π$. 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.
