Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
We write down an explicit conjecture for the instanton partition functions in
4d N=2 SU(N) gauge theories in the presence of a certain type of surface
operator. These surface operators are classified by partitions of N, and for
each partition there is an associated partition function. For the partition N=N
we recover the Nekrasov formalism, and when N=1+...+1 we reproduce the result
of Feigin et. al. For the case N=1+(N-1) our expression is consistent with an
alternative formulation in terms of a restricted SU(N)xSU(N) instanton
partition function. When N=1+...+1+2 the partition functions can also be
obtained perturbatively from certain W-algebras known as quasi-superconformal
algebras, in agreement with a recent general proposal.
Published in 2010.