Integrable structure, Wsymmetry and AGT relation
Abstract
In these notes we consider integrable structure of the conformal field theory with the algebra of symmetries mathcal{A} = {W_n} ⊗ H , where W _{ n } is Walgebra and H is Heisenberg algebra. We found the system of commuting Integrals of Motion with relatively simple properties. In particular, this system has very simple spectrum and the matrix elements of special primary operators between its eigenstates have nice factorized form coinciding exactly with the contribution of the bifundamental multiplet to the Nekrasov partition function for U( n) gauge theories.
 Publication:

Journal of High Energy Physics
 Pub Date:
 January 2012
 DOI:
 10.1007/JHEP01(2012)051
 arXiv:
 arXiv:1109.4042
 Bibcode:
 2012JHEP...01..051F
 Keywords:

 Gauge Symmetry;
 Conformal and W Symmetry;
 Integrable Field Theories;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 JHEP 1201 (2012) 051