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Hints on integrability in the Wilsonian/holographic renormalization group

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The Polchinski equations for the Wilsonian renormalization group in the D-dimensional matrix scalar field theory can be written in a Hamiltonian form, if N is large. 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 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.

This talk is part of the DAMTP Friday GR Seminar series.

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