Hints on integrability in the Holographic RG

          @misc{ pirsa_PIRSA:11060010,
            doi = {10.48660/11060010},
            url = {https://pirsa.org/11060010},
            author = {Akhmedov, Emil},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Hints on integrability in the Holographic RG},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {jun},
            note = {PIRSA:11060010 see, \url{https://pirsa.org}}
          }
          

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 $Tr\phi^n$ (for all $n$) operators. We show that at low energies independently of the dimensionality $D$ the Hamiltonian system in question reduces to the {\it 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.