Boundary correlation numbers in one matrix model

We introduce one matrix model coupled to multi-flavor vectors. The two-flavor vector model is demonstrated to reproduce the two-point correlation numbers of boundary primary fields of two dimensional (2, 2p+1) minimal Liouville gravity on disk, generalizing the loop operator (resolvent) description. The model can properly describe non-trivial boundary conditions for the matter Cardy state as well as for the Liouville field. From this we propose that the n-flavor vector model will be suited for producing the boundary correlation numbers with n different boundary conditions on disk.Comment: 16 pages, 3 figures, add elaboration on matter Cardy state and reference

Holstein-Primakoff Realizations on Coadjoint Orbits

We derive the Holstein-Primakoff oscillator realization on the coadjoint orbits of the $SU(N+1)$ and $SU(1,N)$ group by treating the coadjoint orbits as a constrained system and performing the symplectic reduction. By using the action-angle variables transformations, we transform the original variables into Darboux variables. The Holstein-Primakoff expressions emerge after quantization in a canonical manner with a suitable normal ordering. The corresponding Dyson realizations are also obtained and some related issues are discussed.Comment: 14 pages, Revtex, A minor revision is mad

A note on quality choice with an extended Mussa and Rosen's model

We suggest a model derived from the well-known Mussa and Rosen's model, in which two populations of consumers of opposite tastes co-exist: they rank in exactly the reverse order variants sold at the same price. This model may account for linked and contradictory characteristics in products (as for instance nutritional quality and taste), with consumers attaching more importance to one or to the other aspect. The subgame perfect equilibrium is fully characterized for a costless duopoly choosing qualities then prices.opposite tastes.

Parametric dependence of irregular conformal block

Irregular conformal block is an important tool to study a new type of conformal theories, which can be constructed as the colliding limit of the regular conformal block. The irregular conformal block is realized as the $\beta$-deformed Penner matrix model whose partition function is regarded as the inner product of the irregular modules. The parameter dependence of the inner product is obtained explicitly using the loop equation with close attention to singularities in the parameter space. It is noted that the exact singular structure of the parameter space in general can be found using a very simple and powerful method which uses the flow equations of the partition function together with the hierarchical structure of the singularity. This method gives the exact expression to all orders of large $N$ expansion without using the explicit contour integral of the filling fraction.Comment: 34pages, 8figure