Higher order loop equations for Arand Drquiver matrix models

2003/11/30 by Stefano Chiantese, Albrecht Klemm, Ingo Runkel
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.1088/1126-6708/2004/03/033

published as JHEP 0403 (2004) 033 · 31 pages, 3 figures; v2: added introduction to section 2, version published in JHEP

openalex publication_date 2004/03/11 · arxiv created 2004/03/31 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 A_r and D_r quiver models and check that at large N they are related to a deformation of the corresponding singular Calabi-Yau geometry.

Citations

• Geometric Transitions and N=1 Quiver Theories
• Quivers via anomaly chains
• Gauge invariant matrix model for the Â-D-Ê closed strings
• Breakdown of universality in multi-cut matrix models
• AN INTRODUCTION TO SUPERSYMMETRIC GAUGE THEORIES AND MATRIX MODELS
• THE MODELS OF TWO-DIMENSIONAL CONFORMAL QUANTUM FIELD THEORY WITH Zn SYMMETRY
• W-symmetry in Conformal Field Theory
• Intersection Theory, Integrable Hierarchies and Topological Field Theory