标题： 由D-膜分类Grassmann sigma模型和非阿贝尔规范理论中的双瞬子 显示英文标题

标题： Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes

摘要： 我们将Grassmann $Gr_{N_{\rm F},N_{\rm C}}$ sigma模型（包括 ${\mathbb C}P^{N_{\rm F}-1}$ 模型）中的双瞬子分类，这些模型定义在 ${\mathbb R}^{1}\times S^{1}$ 上，并带有扭边界条件。我们将这些模型表述为具有 $N_{\rm F}$ 种味的 $U(N_{\rm C})$ 规范理论，其中这些味处于基本表示下。这些理论可以被提升为超对称规范理论，而且还可以嵌入到II型超弦理论中的D膜构型里。我们专注于由多个分数瞬子组成的特定构型，即中性双瞬子和带电双瞬子，它们被Ünsal及其合作者识别为微扰红外重整子。我们表明，D膜构型以及模量矩阵提供了一个非常有用的工具，用于分类这些模型中的所有可能的双瞬子构型。与 ${\mathbb C}P^{N_{\rm F}-1}$ 模型不同，在这里存在拓扑荷大于一（数量级为 $N_{\rm C}$）的Bogomol'nyi-Prasad-Sommerfield (BPS) 分数瞬子，这些瞬子不能简化为普通瞬子和分数瞬子的组合。因此，我们发现Grassmann sigma模型允许由BPS和反BPS分数瞬子构成的中性双瞬子，每个分数瞬子的拓扑荷都大于（小于）一（负一），且这些双瞬子无法分解为瞬子-反瞬子对和其他部分。 发现${\mathbb C}P^{N_{\rm F}-1}$模型不存在荷电双瞬子。相比之下，我们发现Grassmann sigma模型允许存在荷电双瞬子，并且我们构造了这些场方程的精确非BPS解。 显示英文摘要

摘要： We classify bions in the Grassmann $Gr_{N_{\rm F},N_{\rm C}}$ sigma model (including the ${\mathbb C}P^{N_{\rm F}-1}$ model) on ${\mathbb R}^{1}\times S^{1}$ with twisted boundary conditions. We formulate these models as $U(N_{\rm C})$ gauge theories with $N_{\rm F}$ flavors in the fundamental representations. These theories can be promoted to supersymmetric gauge theories and further can be embedded into D-brane configurations in type II superstring theories. We focus on specific configurations composed of multiple fractional instantons, termed neutral bions and charged bions, which are identified as perturbative infrared renormalons by \"{U}nsal and his collaborators. We show that D-brane configurations as well as the moduli matrix offer a very useful tool to classify all possible bion configurations in these models. Contrary to the ${\mathbb C}P^{N_{\rm F}-1}$ model, there exist Bogomol'nyi-Prasad-Sommerfield (BPS) fractional instantons with topological charge greater than unity (of order $N_{\rm C}$) that cannot be reduced to a composite of an instanton and fractional instantons. As a consequence, we find that the Grassmann sigma model admits neutral bions made of BPS and anti-BPS fractional instantons each of which has topological charge greater (less) than one (minus one), that are not decomposable into instanton anti-instanton and the rests. The ${\mathbb C}P^{N_{\rm F}-1}$ model is found to have no charged bions. In contrast, we find that the Grassmann sigma model admits charged bions, for which we construct exact non-BPS solutions of the field equations.