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Testing the Bethe ansatz with large N renormalons
The European Physical Journal Special Topics ( IF 2.8 ) Pub Date : 2021-08-12 , DOI: 10.1140/epjs/s11734-021-00252-4
Marcos Mariño 1 , Ramon Miravitllas 1 , Tomás Reis 1
Affiliation  

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/N 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 N 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/N expansion.



中文翻译:

用大 N 重整子测试 Bethe ansatz

一旦理论通过守恒电荷耦合到外部电位,就可以使用 Bethe ansatz 推测性计算可积渐近自由理论的基态能量。这导致对能量的微扰膨胀的精确预测。我们在非线性 sigma 模型及其超对称扩展中提供了对这种预测的非平凡测试,方法是在 1 / N扩展中以次前导顺序和所有循环分析计算相关联的费曼图。通过研究图的大阶行为,我们定位了理论重整子的位置,并获得了大N的解析表达式与每个相关联的反系列。作为我们计算的衍生产品,我们提供了这些理论的 beta 函数的直接推导,在 1 / N扩展中的次领先顺序。

更新日期:2021-08-12
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