Counting monster potentials
Counting monster potentials
复制标题
计算怪物潜力
DOI：
10.1007/jhep02(2021)059
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发表时间：
2020
影响因子：
5.4
通讯作者：
D. Masoero
中科院分区：
文献类型：
--
作者：
R. Conti;D. Masoero
我们研究了Bazhanov-Lukyanov-Zamolodchikov的巨势的大动量极限，根据ODE/IM对应，它应该对应于量子KdV模型的激发态。我们证明了这些势的极点在基态势的复平衡态上渐近凝聚，并用厄米特多项式的朗斯基根表示了对这些渐近性的主要修正。这使我们能够将N的每个分划与N个根的唯一的怪物势相关联，我们计算它的谱。因此，我们证明了——直到一些数学技术——固定一个整数N，具有N根的怪物势的数量与N的整数分区的数量一致，N是量子KdV模型的N级子空间的维度。与ODE/IM通信完全一致。
We study the large momentum limit of the monster potentials of Bazhanov-Lukyanov-Zamolodchikov, which — according to the ODE/IM correspondence — should correspond to excited states of the Quantum KdV model. We prove that the poles of these potentials asymptotically condensate about the complex equilibria of the ground state potential, and we express the leading correction to such asymptotics in terms of the roots of Wronskians of Hermite polynomials. This allows us to associate to each partition of N a unique monster potential with N roots, of which we compute the spectrum. As a consequence, we prove — up to a few mathematical technicalities — that, fixed an integer N , the number of monster potentials with N roots coincides with the number of integer partitions of N , which is the dimension of the level N subspace of the quantum KdV model. In striking accordance with the ODE/IM correspondence.