  For six dimensional nilmanifolds we build a module $\mathcal{H}$ of an affine
Kac Moody vertex algebras. Then, we associate some logarithmic fields for the
module $\mathcal{H}$ and we study their singularities. We also presented a
physics motivation behind this construction.
  We study a particular case, we show that when the nilmanifold $N$ is a $k$
degree $S^1$--fibration over the two torus and a choice of $l \in \mathbb{Z}
\simeq H^3(N, \mathbb{Z})$ the fields associated to the space $\mathcal{H}$
have tri-logarithm singularities whenever $kl \neq 0$.
