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arXiv · 1809.10832

Nilmanifolds and their associated non local fields

Juan Jose Villarreal
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Abstract

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 $kl \neq 0$.

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Juan Jose Villarreal. 2018-09-28. Nilmanifolds and their associated non local fields. https://arxiv.org/abs/1809.10832

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