PIRSA:11060010 Scientific Series Quantum Fields and Strings

DOI10.48660/11060010

Series: Quantum Fields and Strings

Akhmedov, E. (2011). Hints on integrability in the Holographic RG. Perimeter Institute. https://pirsa.org/11060010

Akhmedov, Emil. Hints on integrability in the Holographic RG. Perimeter Institute, Jun. 14, 2011, https://pirsa.org/11060010 

@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.

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