1992/01/08 by S. Kharchev, A. Marshakov, A. Mironov +4 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Scaling #Scaling limit #hep-th
paper · pdf · doi:10.1016/0550-3213(92)90521-c
published as Nucl.Phys.B380:181-240,1992 · 67 pages (October 1991)
arxiv created 1992/01/08 · openalex publication_date 1992/08/01 · arxiv updated 2011/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a new 1-matrix model with arbitrary potential and the matrix-valued background field. Its partition function is a τ-function of KP-hierarchy, subjected to a kind of \cal L-1-constraint. Moreover, partition function behaves smoothly in the limit of infinitely large matrices. If the potential is equal to XK+1, this partition function becomes a τ-function of K-reduced KP-hierarchy, obeying a set of \cal W K-algebra constraints identical to those conjectured in \citeFKN91 for double-scaling continuum limit of (K-1)-matrix model. In the case of K=2 the statement reduces to the early established \citeMMM91b relation between Kontsevich model and the ordinary 2d quantum gravity . Kontsevich model with generic potential may be considered as interpolation between all the models of 2d quantum gravity with c<1 preserving the property of integrability and the analogue of string equation.