Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Refined BPS state counting from Nekrasov's formula and Macdonald
  functions   It has been argued that the 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 proposed before (hep-th/0502061) is a building block of
the Nekrasov's partition function with two equivariant parameters. Compared
with another refined topological vertex by Iqbal-Kozcaz-Vafa (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 C^2. 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.

32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess