Hints on integrability in the Wilsonian/holographic renormalization group
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 Trϕ n (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.