Baryonic Generating Functions

We show how it is possible to use the plethystic program in order to compute baryonic generating functions that count BPS operators in the chiral ring of quiver gauge theories living on the world volume of D branes probing a non compact CY manifold. Special attention is given to the conifold theory and the orbifold C^2/Z_2 times C, where exact expressions for generating functions are given in detail. This paper solves a long standing problem for the combinatorics of quiver gauge theories with baryonic moduli spaces. It opens the way to a statistical analysis of quiver theories on baryonic branches. Surprisingly, the baryonic charge turns out to be the quantized Kahler modulus of the geometry.Comment: 44 pages, 7 figures; fonts change

Generating Functions for Coherent Intertwiners

We study generating functions for the scalar products of SU(2) coherent intertwiners, which can be interpreted as coherent spin network evaluations on a 2-vertex graph. We show that these generating functions are exactly summable for different choices of combinatorial weights. Moreover, we identify one choice of weight distinguished thanks to its geometric interpretation. As an example of dynamics, we consider the simple case of SU(2) flatness and describe the corresponding Hamiltonian constraint whose quantization on coherent intertwiners leads to partial differential equations that we solve. Furthermore, we generalize explicitly these Wheeler-DeWitt equations for SU(2) flatness on coherent spin networks for arbitrary graphs.Comment: 31 page

Some generating functions for q-polynomials

We obtain q-analogues of the Sylvester, Ces\`aro, Pasternack, and Bateman polynomials. We also derive generating functions for these polynomials.Comment: 10 page