Notes on Mayer expansions and matrix models

DOI10.1016/J.NUCLPHYSB.2014.01.017zbMATH Open1284.82030arXiv1310.3566OpenAlexW2156819829MaRDI QIDQ2441705

Author name not available (Why is that?)

Publication date: 27 March 2014

Published in: (Search for Journal in Brave)

Abstract: Mayer cluster expansion is an important tool in statistical physics to evaluate grand canonical partition functions. It has recently been applied to the Nekrasov instanton partition function of $mathcalN=2$ 4d gauge theories. The associated canonical model involves coupled integrations that take the form of a generalized matrix model. It can be studied with the standard techniques of matrix models, in particular collective field theory and loop equations. In the first part of these notes, we explain how the results of collective field theory can be derived from the cluster expansion. The equalities between free energies at first orders is explained by the discrete Laplace transform relating canonical and grand canonical models. In a second part, we study the canonical loop equations and associate them to similar relations on the grand canonical side. It leads to relate the multi-point densities, fundamental objects of the matrix model, to the generating functions of multi-rooted clusters. Finally, a method is proposed to derive loop equations directly on the grand canonical model.

Full work available at URL: https://arxiv.org/abs/1310.3566

Mathematics Subject Classification ID

No records found.

This page was built for publication: Notes on Mayer expansions and matrix models

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2441705)