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Hints on integrability in the Wilsonian/holographic renormalization group

  • Methods of Theoretical Physics
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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.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow region, 141700, Russia

    E. T. Akhmedov & E. T. Musaev

  2. National University of Science and Technology MISiS, Moscow, 119049, Russia

    I. B. Gahramanov

  3. Institute for Theoretical and Experimental Physics, Moscow, 117218, Russia

    E. T. Akhmedov & E. T. Musaev

Authors
  1. E. T. Akhmedov
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  2. I. B. Gahramanov
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  3. E. T. Musaev
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Correspondence to E. T. Akhmedov.

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Akhmedov, E.T., Gahramanov, I.B. & Musaev, E.T. Hints on integrability in the Wilsonian/holographic renormalization group. Jetp Lett. 93, 545–550 (2011). https://doi.org/10.1134/S0021364011090037

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  • DOI: https://doi.org/10.1134/S0021364011090037

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