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

Abstract

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 $\mathcal{O}$. We determine these operators and show that they are particular composites of q-deformed hierarchical vertex operators , with a positive integer p. In agreement with literature's results, we find that G${}_d(q)$, $d\ge 4$, cannot be the generating functional of all \textit{d- dimensional} generalized Young diagrams .

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

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