Hints on integrability in the Wilsonian/holographic renormalization group

Details Hints on integrability in the Wilsonian/holographic renormalization group Hints on integrability in the Wilsonian/holographic renormalization group

2010-06-10

arxiv.org/abs/1006.1970v5

JETP Lett.93:545-550,2011

Physics

High Energy Physics

High Energy Physics - Theory

9 pages. Arguments are expanded. Higher derivative operators are included

Scientific paper

10.1134/S0021364011090037

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 complete basis of single trace operators. We show that at low energies independently of the dimensionality $D$ the Hamiltonian system in question (for the subsector of operators without derivatives) reduces to the {\it integrable} effective theory. The obtained Hamiltonian system describes large wavelength KdV type (Burger--Hopf) equation and is related to the effective theory obtained by Das and Jevicki for the matrix quantum mechanics.

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