Refined matrix models from BPS counting

Abstract

We construct a free fermion and matrix model representation of refined BPS generating functions of D2 and D0 branes bound to a single D6 brane, in a class of toric manifolds without compact four-cycles. In appropriate limit we obtain a matrix model representation of refined topological string amplitudes. We consider a few explicit examples which include a matrix model for the refined resolved conifold, or equivalently five-dimensional U(1) gauge theory, as well as a matrix representation of the refined MacMahon function. Matrix models which we construct have ordinary unitary measure, while their potentials are modified to incorporate the effect of the refinement.

27 pages, 4 figures, published version

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Cited by in corpus (10)

• Proving AGT conjecture as HS duality: extension to five dimensions
• A slow review of the AGT correspondence
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• Quantum curves and conformal field theory
• Comment on integrability in Dijkgraaf-Vafa beta-ensembles
• Challenges of beta-deformation
• The remodeling conjecture and the Faber-Pandharipande formula
• BPS states, crystals and matrices
• Dijkgraaf-Vafa conjecture and beta-deformed matrix models