论文标题
旋律图的动机
Motives of melonic graphs
论文作者
论文摘要
我们研究了旋律图的仿射图超曲面补充的呈递归关系。我们针对几个旋速图的家族明确计算这些类别，重点是价值$ 4 $内部顶点的图形，与CTKT张量型模型有关。结果暗示了一个复杂而有趣的结构，即不同家族的图形类别之间的分裂性关系或非平凡关系。使用递归关系，我们证明了所有旋速图的Grothendieck类都是阳性的，作为模量空间$ \ MATHCAL M_ {0,4} $类别的多项式。我们还猜想，基于数百个显式计算，相应的多项式是对数孔腔。
We investigate recursive relations for the Grothendieck classes of the affine graph hypersurface complements of melonic graphs. We compute these classes explicitly for several families of melonic graphs, focusing on the case of graphs with valence-$4$ internal vertices, relevant to CTKT tensor models. The results hint at a complex and interesting structure, in terms of divisibility relations or nontrivial relations between classes of graphs in different families. Using the recursive relations we prove that the Grothendieck classes of all melonic graphs are positive as polynomials in the class of the moduli space $\mathcal M_{0,4}$. We also conjecture that the corresponding polynomials are log-concave, on the basis of hundreds of explicit computations.
