REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS

By H. Awata, H. Kanno. 2008

178 citations recorded by the source corpus.

It has been argued that Nekrasov's partition function gives the generating function of refined BPS state counting in the compactification of M theory on local Calabi–Yau spaces. We show that a refined version of the topological vertex we previously proposed (arXiv:hep-th/0502061) is a building block of Nekrasov's partition function with two equivariant parameters. Compared with another refined topological vertex by Iqbal, Kozcaz and Vafa (arXiv:hep-th/0701156), our refined vertex is expressed entirely in terms of the specialization of the Macdonald symmetric functions which is related to the equivariant character of the Hilbert scheme of points on ℂ2. We provide diagrammatic rules for computing the partition function from the web diagrams appearing in geometric engineering of Yang–Mills theory with eight supercharges. Our refined vertex has a simple transformation law under the flop operation of the diagram, which suggests that homological invariants of the Hopf link are related to the Macdonald functions.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/652d7d9a51c36338bc0a6a1370636c4171647ec4

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Citations in the corpus

The Ω Deformed B-model for Rigid N = 2 Theories (2011, background): “1) can be interpreted as a supersymmetric index which counts refined BPS numbers for D2/D0 bound states on M associated to D2 branes with charge β ∈ H 2 (M,Z) labelled by the powers of e t [19, 20].”
Knot Homology from Refined Chern-Simons Theory (2011, background): “As explained in [1], to solve a topological field theory on any three-manifold with arbitrary knots inside one needs the S and T matrices, 1 For other work on refined open topological string partition functions see [23,24,25].”
On instantons as Kaluza-Klein modes of M5-branes (2011, methodology): “For SU(2) pure N =2 Yang-Mills theory in 5 dimensions, [46] used their ‘trace identities’ in topological vertex formulation to rewrite the instanton partition function into an infinite product form which clearly shows zsp.”
Five-dimensional AGT conjecture and the deformed Virasoro algebra (2009, background): “In [25]–[27] it was argued that they are closely related with the Macdonald symmetric polynomials [28].”