46 research outputs found
Symplectic invariants, Virasoro constraints and Givental decomposition
Following the works of Alexandrov, Mironov and Morozov, we show that the
symplectic invariants of \cite{EOinvariants} built from a given spectral curve
satisfy a set of Virasoro constraints associated to each pole of the
differential form and each zero of . We then show that they satisfy
the same constraints as the partition function of the Matrix M-theory defined
by Alexandrov, Mironov and Morozov. The duality between the different matrix
models of this theory is made clear as a special case of dualities between
symplectic invariants. Indeed, a symplectic invariant admits two decomposition:
as a product of Kontsevich integrals on the one hand, and as a product of 1
hermitian matrix integral on the other hand. These two decompositions can be
though of as Givental formulae for the KP tau functions.Comment: 19 page
Topological expansion and boundary conditions
In this article, we compute the topological expansion of all possible
mixed-traces in a hermitian two matrix model. In other words we give a recipe
to compute the number of discrete surfaces of given genus, carrying an Ising
model, and with all possible given boundary conditions. The method is
recursive, and amounts to recursively cutting surfaces along interfaces. The
result is best represented in a diagrammatic way, and is thus rather simple to
use.Comment: latex, 25 pages. few misprints correcte
Loop equations for the semiclassical 2-matrix model with hard edges
The 2-matrix models can be defined in a setting more general than polynomial
potentials, namely, the semiclassical matrix model. In this case, the
potentials are such that their derivatives are rational functions, and the
integration paths for eigenvalues are arbitrary homology classes of paths for
which the integral is convergent. This choice includes in particular the case
where the integration path has fixed endpoints, called hard edges. The hard
edges induce boundary contributions in the loop equations. The purpose of this
article is to give the loop equations in that semicassical setting.Comment: Latex, 20 page