Hints on integrability in the Wilsonian/holographic renormalization group

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 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.

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

References in corpus (1)

• An exact statement for Wilsonian and Holographic renormalization group

Cited by in corpus (12)

• Wilsonian renormalisation and the exact cut-off scale from holographic duality
• Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly
• Holographic Wilson's RG
• Higher Spin vs. Renormalization Group Equations
• Holographic RG flows and boundary conditions in a 3D gauged supergravity
• Connecting the Holographic and Wilsonian Renormalization Groups
• Bulk Gauge Fields and Holographic RG from Exact RG
• Holographic RG from ERG: Locality and General Coordinate Invariance in the Bulk
• On Functional Hamilton-Jacobi and Schrödinger Equations and Functional Renormalization Group
• A Note on Efimov Nonlocal and Nonpolynomial Quantum Scalar Field Theory
• The Static Heavy Quark-Antiquark Potential within String Theory in Arbitrary Stationary Backgrounds
• $SO(1,d+1)$ symmetry of the Exact RG equation