标题： 大N矢量模型在哈密顿框架中 显示英文标题

标题： Large N vector models in the Hamiltonian framework

摘要： 我们提出了一种波动的$N$形式，基于二次量子化，用于通过哈密顿方法从场论中描述大的$N$向量模型。 我们首先在具有四次相互作用的量子力学系统中介绍该方法，然后将这些技术应用于$O(N)$模型在$2+1$和$3+1$维度中的情况。 我们恢复了各种已知结果，例如确定系统基态的间隙方程、负耦合下的束缚态存在以及临界指数的主要贡献，并提供了在非局部相互作用存在的情况下，大的$N$路径积分鞍点作为扩展物体的玻色-爱因斯坦凝聚的解释。 在大 $N$ 极限下，这种形式主义自然地以双局域场来描述基本的 $O(N)$ 对称激发，这些双局域场是 $\text{AdS}_4/\text{CFT}_3$ 对 $O(N)$ 模型和瓦西列夫引力研究的基础。 显示英文摘要

摘要： We present a fluctuating $N$ formalism, based on second-quantization, to describe large $N$ vector models from field theory using Hamiltonian methods. We first present the method in the simpler setting of a quantum mechanical system with quartic interactions, and then apply these techniques to the $O(N)$ model in $2+1$ and $3+1$ dimensions. We recover various known results, such as the gap equation determining the ground state of the system, the presence of bound states at negative coupling and the leading order contribution to critical exponents, and provide an interpretation of the large $N$ path integral saddle point as a Bose-Einstein condensate of extended objects in the presence of a non-local interaction. In the large $N$ limit, this formalism leads naturally to a description of elementary $O(N)$ symmetric excitations in terms of bilocal fields, which are at the basis of $\text{AdS}_4/\text{CFT}_3$ studies of the $O(N)$ model and Vasiliev gravity.