Mariño Marcos, Miravitllas Ramon, Reis Tomás
Département de Physique Théorique et Section de Mathématiques, Université de Genève, 1211 Geneva, Switzerland.
Eur Phys J Spec Top. 2021;230(12-13):2641-2666. doi: 10.1140/epjs/s11734-021-00252-4. Epub 2021 Aug 12.
The ground-state energy of integrable asymptotically free theories can be conjecturally computed using the Bethe ansatz once the theory has been coupled to an external potential through a conserved charge. This leads to a precise prediction for the perturbative expansion of the energy. We provide a non-trivial test of this prediction in the non-linear sigma model and its supersymmetric extension, by calculating analytically the associated Feynman diagrams at next-to-leading order in the 1/ expansion, and at all loops. By investigating the large order behavior of the diagrams, we locate the position of the renormalons of the theory and we obtain an analytic expression for the large trans-series associated to each. As a spin-off of our calculation, we provide a direct derivation of the beta function of these theories, at next-to-leading order in the 1/ expansion.
一旦可积渐近自由理论通过一个守恒荷与外部势耦合，其基态能量就可以通过贝塞耳假设推测性地计算出来。这就对能量的微扰展开给出了精确预测。我们在非线性西格玛模型及其超对称扩展中对这一预测进行了非平凡检验，通过在1/展开的次领头阶以及所有圈阶上解析计算相关的费曼图。通过研究这些图的高阶行为，我们确定了该理论重整子的位置，并得到了与每个重整子相关的大阶次超越级数的解析表达式。作为我们计算的一个附带成果，我们在1/展开的次领头阶上直接推导了这些理论的β函数。
