Hints on integrability in the Wilsonian/holographic renormalization group
Hints on integrability in the Wilsonian/holographic renormalization group
复制标题
关于威尔逊/全息重正化群中可积性的提示
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
E. Musaev
中科院分区：
文献类型：
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作者：
E. Akhmedov;I. Gahramanov;E. Musaev
D维矩阵标量场理论中威尔逊重整化群的Polchinski方程在N大时可以写成哈密顿形式。哈密顿量定义了沿沿着一个额外的全息维度（能量标度）的演化，并且可以精确地找到Tr n（对于所有n）算子的子扇区。我们表明，在低能量独立的维数D的哈密顿系统的问题减少到可积的有效理论。所得到的哈密顿系统描述了具有外部势的大波长KdV型（Burger-Hopf）方程，并与Das和Jevicki的矩阵量子力学有效理论有关.
The Polchinski equations for the Wilsonian renormalization group in the D-dimensional matrix scalar field theory can be written at large N in a Hamiltonian form. The Hamiltonian defines evolution along one extra holographic dimension (energy scale) and can be found exactly for the subsector of Trϕn (for all n) operators. We show that at low energies independently of the dimensionality D the Hamiltonian system in question reduces to the integrable effective theory. The obtained Hamiltonian system describes large wavelength KdV type (Burger-Hopf) equation with an external potential and is related to the effective theory obtained by Das and Jevicki for the matrix quantum mechanics.