Hints on integrability in the Wilsonian/holographic renormalization group
E. T. Akhmedov*∇, I. B. Gahramanov† 1), E. T. Musaev*∇ 1)
*Moscow Institute of Physics and Technology, Dolgoprudny, Moscow reg., Russia
†National University of Science and Technology "MISIS", Moscow, Russia
∇Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia
Abstract
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.