Higher order loop equations for Ar and Dr quiver matrix models
Stefano Chiantese, Albrecht Klemm, Ingo Runkel
Abstract
We use free boson techniques to investigate A-D-E-quiver matrix models. Certain higher spin fields in the free boson formulation give rise to higher order loop equations valid at finite N. These fields form a special kind of W-algebra, called Casimir algebra. We compute explicitly the loop equations for Ar and Dr quiver models and check that at large N they are related to a deformation of the corresponding singular Calabi-Yau geometry.
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