Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On combinatorial expansion of the conformal blocks arising from AGT
  conjecture   In their recent paper \cite{Alday:2009aq} Alday, Gaiotto and Tachikawa
proposed a relation between $\mathcal{N}=2$ four-dimensional supersymmetric
gauge theories and two-dimensional conformal field theories. As part of their
conjecture they gave an explicit combinatorial formula for the expansion of the
conformal blocks inspired from the exact form of instanton part of the Nekrasov
partition function. In this paper we study the origin of such an expansion from
a CFT point of view. We consider the algebra $\mathcal{A}=\text{\sf
Vir}\otimes\mathcal{H}$ which is the tensor product of mutually commuting
Virasoro and Heisenberg algebras and discover the special orthogonal basis of
states in the highest weight representations of $\mathcal{A}$. The matrix
elements of primary fields in this basis have a very simple factorized form and
coincide with the function called $Z_{\text{\sf{bif}}}$ appearing in the
instanton counting literature. Having such a simple basis, the problem of
computation of the conformal blocks simplifies drastically and can be shown to
lead to the expansion proposed in \cite{Alday:2009aq}. We found that this basis
diagonalizes an infinite system of commuting Integrals of Motion related to
Benjamin-Ono integrable hierarchy.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph