Detailed study of a transition point in the Veneziano-Wosiek model of Planar Quantum Mechanics

On the supersymmetric vacua of the Veneziano-Wosiek model

We study the supersymmetric vacua of the Veneziano-Wosiek model in sectors with fermion number F=2, 4 at finite 't Hooft coupling lambda. We prove that for F=2 there are two zero energy vacua for lambda > lambda_c = 1 and none otherwise. We give the analytical expressions of both vacua. One of them was previously known, the second one is obtained by solving the cohomology of the supersymmetric charges. At F=4 we compute the would-be supersymmetric vacua at high order in the the strong coupling expansion and provide strong support to the conclusion that lambda = 1 is a critical point in this se…

超对称大-$N$量子力学中的Krylov复杂度

Krylov Complexity in Supersymmetric Large-$N$ Quantum Mechanics

研究超对称矩阵量子力学Veneziano-Wosiek模型在大$N$平面极限下的Krylov复杂度，发现临界耦合$\lambda=1$处复杂度呈二次增长，并通过可解模型获得解析理解。

Veneziano振幅的六点一致性与唯一性

Six-point consistency and uniqueness of the Veneziano amplitude

本文通过结合六点一致性与低阶超对称关系，在亚纯类中证明Veneziano四点振幅的唯一性，并确定其全部极点与留数。

The planar spectrum in U(N)-invariant quantum mechanics by Fock space methods: I. The bosonic case

Prompted by recent results on Susy-U(N)-invariant quantum mechanics in the large N limit by Veneziano and Wosiek, we have examined the planar spectrum in the full Hilbert space of U(N)-invariant states built on the Fock vacuum by applying any U(N)-invariant combinations of creation-operators. We present results about 1) the supersymmetric model in the bosonic sector, 2) the standard quartic Hamiltonian. This latter is useful to check our techniques against the exact result of Brezin et al. The SuSy case is where Fock space methods prove to be the most efficient: it turns out that the problem i…