论文标题
来自Associahedra，Cyclohedra和Personized Persutohedra
Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra
论文作者
论文摘要
Stringy Canonical形式是一类积分，可提供任何多面体的规范形式的$α'$变形。对于有限型群集代数的广义联想，存在完全刚性的弦乐积分，其配置空间是所谓的二进制几何形状，而对于经典类型，粒子和字符串的散射与经典类型有关。在本文中，我们为另一类的多型Permutohedra提出了一大批刚性的弦乐规范，其中还包括Associahedra和Cyclohedra作为特殊情况（类型$ a_n $和$ b_n $ nerverized centryized aSsociahedra）。值得注意的是，我们发现此类积分的配置空间也是二进制几何形状，怀疑仅适用于广义合并。对于任何可以写入Minkowski坐标简式总和的通用定位符，我们表明，其刚性的积分分配给有限$α'$的无质量杆的较低积分的产品，尽管配置空间是二进制的二进制，尽管$ u $方程比“完美的”群集病例更具通用形式。此外，我们提供了一个无限类的示例，该示例通过$ a_n $和$ b_n $积分的类型的变性获得，它们也具有完美的$ u $ quations。我们的结果为通常的字符串积分和模量空间提供了另一个概括，其物理解释仍有待探索。
Stringy canonical forms are a class of integrals that provide $α'$-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebra, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type $A_n$ and $B_n$ generalized associahedra). Remarkably, we find that the configuration spaces of such integrals are also binary geometries, which were suspected to exist for generalized associahedra only. For any generalized permutohedron that can be written as Minkowski sum of coordinate simplices, we show that its rigid stringy integral factorizes into products of lower integrals for massless poles at finite $α'$, and the configuration space is binary although the $u$ equations take a more general form than those "perfect" ones for cluster cases. Moreover, we provide an infinite class of examples obtained by degenerations of type $A_n$ and $B_n$ integrals, which have perfect $u$ equations as well. Our results provide yet another family of generalizations of the usual string integral and moduli space, whose physical interpretations remain to be explored.
