Soft Matrix Models and ChernSimons Partition Functions
Abstract
We study the properties of matrix models with soft confining potentials. Their precise mathematical characterization is that their weight function is not determined by its moments. We mainly rely on simple considerations based on orthogonal polynomials and the moment problem. In addition, some of these models are equivalent, by a simple mapping, to matrix models that appear in ChernSimons theory. The models can be solved with q deformed orthogonal polynomials (StieltjesWigert polynomials), and the deformation parameter turns out to be the usual q parameter in ChernSimons theory. In this way, we give a matrix model computation of the ChernSimons partition function on S^{3} and show that there are infinitely many matrix models with this partition function.
 Publication:

Modern Physics Letters A
 Pub Date:
 2004
 DOI:
 10.1142/S0217732304014100
 arXiv:
 arXiv:hepth/0212128
 Bibcode:
 2004MPLA...19.1365T
 Keywords:

 11.10.Kk;
 11.15.Tk;
 02.30.f;
 02.10.Kn;
 Field theories in dimensions other than four;
 Other nonperturbative techniques;
 Function theory analysis;
 Knot theory;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 13 pages, 3 figures