Hermitian versus anti-Hermitian one matrix models and their hierarchies

Sep, 1991
34 pages
Published in:
  • Nucl.Phys.B 373 (1992) 247-280
  • Published: 1992
e-Print:
Report number:
  • IASSNS-HEP-91-59,
  • PUPT-1280

Citations per year

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Abstract: (Elsevier)
Building on a recent work of Č. Crnković, M. Douglas and G. Moore, a study of multi-critical multi-cut one-matrix models and their associated sl(2, C ) integrable hirarchies, is further pursued. The double-scaling limits of hermitian matrix models with different scaling ansätze, lead to the KdV hierarchy, to the modified KdV hierarchy and part of the non-linear Schrödinger hierarchy. Instead, the anti-hermitian matrix model, in the 2-arc sector, results in the Zakharov-Shabat hierarchy, which contains both KdV and mKdV as reductions. For all the hierarchies it is found that the Virasoro constraints act on the associated τ-functions. Whereas it is known that the ZS and KdV models lead to the Virasoro constraints of an sl(2, C ) vacuum, we find that the mKdV model leads to the Virasoro constraints of a highest-weight state with arbitrary conformal dimension.
  • matrix model
  • critical phenomena
  • Korteweg-de Vries equation
  • Schroedinger equation: nonlinear
  • differential equations: hierarchy
  • symmetry: SL(2,C)
  • constraint: Virasoro
  • differential equations: string