Generalized MacMahon G(q) as q-deformed CFT Correlation Function

Details Generalized MacMahon G(q) as q-deformed CFT Correlation Function Generalized MacMahon G(q) as q-deformed CFT Correlation Function

2008-01-17

arxiv.org/abs/0801.2661v2

Nucl.Phys.B801:316-345,2008

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, Appendix B shortened, references updated, To appear in NPB

Scientific paper

10.1016/j.nuclphysb.2008.03.006

Using $\Gamma_{\pm}(z) $ vertex operators of the $c=1$ two dimensional conformal field theory, we give a 2d-quantum field theoretical derivation of the conjectured d- dimensional MacMahon function G$_{d}(q) $. We interpret this function G$_{d}(q) $ as a $(d+1) $- point correlation function $\mathcal{G}_{d+1}(z_{0},...,z_{d}) $ of some local vertex operators $\mathcal{O}%_{j}(z_{j}) $. We determine these operators and show that they are particular composites of q-deformed hierarchical vertex operators $% \Gamma _{\pm}^{(p)}$, with a positive integer p. In agreement with literature's results, we find that G$_{d}(q) $, $d\geq 4$, cannot be the generating functional of all \textit{d- dimensional} generalized Young diagrams .

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