AGT, N-Burge partitions and W-N minimal models

作者：Belavin Vladimir^*; Foda Omar; Santachiara Raoul

来源：The Journal of High Energy Physics, 2015, 2015(10): 073.

DOI：10.1007/JHEP10(2015)073

• Conformal and W Symmetry
• Integrable Field Theories

Let B-N,n(p,p',H) be a conformal block, with n consecutive channels x(i), t-1, ... , n. in the conformal field theory M-N(p,p') x M-H , M-N(p,p') is a W-N minimal model, generated by chiral spin-2, ..., spin-N currents, and labeled by two co-prime integers p and p', 1 < p <p' while M-H is a free boson conformal field theory. B-N,n(p,p',H) is the expectation value of vertex operators between an initial and a final state. Each vertex operator is labelled by a charge vector that lives in the weight lattice of the Lie algebra A(N-1), spanned by weight vectors (omega) over right arrow (1), ... , (omega) over right arrow (N-1),, We restrict our attention to conformal blocks with vertex operators whose charge vectors point along The charge vectors that label the initial and final states can point in any direction. Following the WN ACT correspondence, and using Nekrasov's instanton partition functions without modification to compute B-N,n(p,p',H) leads to ill-defined expressions. We show that restricting the states that flow in the channels chi(i) , i = 1, ... n, to states labeled by N partitions that we call N-Burge partitions, that satisfy conditions that we call N-Burge conditions, leads to well-defined expressions that we propose to identify with B-N,n(p,p',H) We check our identification by showing that a non-trivial conformal block that we compute, using the N-Burge conditions satisfies the expected differential equation. Further, we check that the generating functions of triples of Young diagrams that obey 3-Burge conditions coincide with characters of degenerate W-3 irreducible highest weight representations.

• 出版日期2015-10-12