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 .
Categories: hep-th
