Generalized MacMahon Gd(q) as q-deformed CFT2 correlation function

Using Γ±(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 Gd(q). We interpret this function Gd(q) as a (d+1)-point correlation function Gd+1(z0,…,zd) of some local vertex operators Oj(zj). We determine these operators and show that they are particular composites of q-deformed hierarchical vertex operators Γ±(p), with a positive integer p. In agreement with literature's results, we find that Gd(q), d⩾4, cannot be the generating functional of all d-dimensional generalized Young diagrams.