Instanton counting, Macdonald function and the moduli space of D-branes
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We argue the connection of Nekrasov's partition function in the Ω background and the moduli space of D-branes, suggested by the idea of geometric engineering and Gopakumar-Vafa invariants. In the instanton expansion of = 2 SU(2) Yang-Mills theory the Nakrasov's partition function with equivariant parameters 1,2 of toric action on 2 factorizes correctly as the character of SU(2)L × SU(2)R spin representation. We show that up to two instantons the spin contents are consistent with the Lefschetz action on the moduli space of D2-branes on (local) F0. We also present an attempt at constructing a refined topological vertex in terms of the Macdonald function. The refined topological vertex with two parameters of T2 action allows us to obtain the generating functions of equivariant χy and elliptic genera of the Hilbert scheme of n points on 2 by the method of topological vertex.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/26cfbcd217bf8ec2a3f26cd717ec122396152cad
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In Geometry and Topology
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Non-Lagrangian theories from brane junctions (2013, unknown): “1 1−Qti −1 λtj qj−µi 1−Qti−1qj = Y (i,j)∈λ (1 −Qtµtj−iqλi−j+1) Y (i,j)∈µ (1 −Qt−λtj+i−1q−µi+j). (A.1) We also occasionally use the Macdonald polynomials Pν(x;t,q). Our main reference is appendix B in [84]. We reproduce here the formulas that we need. We can relate the Macdonald polynomials, at speci”
- Refined Topological Vertex and Instanton Counting (2007, methodology): “Few attempts were made for defining the 2-parameter extension of topological strings and formulating the algorithmical techniques to caluculate the extended partition function [11][16][17].”
- REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS (2008, methodology): “In [14] we reported some results for SU(2) theory with no Chern-Simons coupling.”
- Vortex Counting and Lagrangian 3-Manifolds (2010, background): “mplest possibility: an elementary surface operator in pure N= 2 Maxwell theory, i.e. with abelian gauge group G = U(1). The gauge theory is 7An alternative formulation of the rened vertex appears in [40], but its applicability is apparently no broader than the vertex of [39]. { 27 { Figure 7: A simp”