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Nilmanifolds and their associated non-local fields
Advances in Theoretical and Mathematical Physics ( IF 1.0 ) Pub Date : 2020-01-01 , DOI: 10.4310/atmp.2020.v24.n4.a5
Juan J. Villarreal 1
Affiliation  

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 $kl \neq 0$.

中文翻译:

Nilmanifolds 及其相关的非局部场

对于六维 nilmanifolds,我们构建了一个仿射 Kac Moody 顶点代数的模块 $\mathcal{H}$。然后,我们为模块 $\mathcal{H}$ 关联一些对数域,并研究它们的奇点。我们还提出了这种结构背后的物理动机。我们研究了一个特殊情况,我们证明了当 nilmanifold $N$ 是 $k$ 度时 $S^1$--两个圆环上的纤维化和 $l \in \mathbb{Z} \simeq H^ 3(N, \mathbb{Z})$ 与空间 $\mathcal{H}$ 相关联的字段在 $kl \neq 0$ 时具有三对数奇点。
更新日期:2020-01-01
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