论文标题
6D scfts的椭圆爆炸方程。 iv：很重要
Elliptic Blowup Equations for 6d SCFTs. IV: Matters
论文作者
论文摘要
鉴于最近的几何分类为6d $（1,0）$ scfts，一个主要问题是如何为这个大型班级计算其椭圆形属。后者编码了SCFT的精制BPS谱，该频谱决定了相关的椭圆形非紧凑型Calabi-yau三倍的几何不变。在本文中，我们在原子分类爆炸方程中为所有6d $（1,0）$ scfts建立，这些方程式在很大程度上固定了这些椭圆形属。后者分为两种类型：统一和消失的爆炸方程。对于几乎所有排名一个理论，我们都会发现统一爆炸方程完全决定了椭圆形属。我们开发了几种技术来计算爆炸方程中的椭圆形属和BPS不变性，包括有关字符串数量的递归公式，Weyl Orbit扩展，精制的BPS扩展以及$ε_1，ε_2$扩展。对于高级理论，我们提出了一个粘合规则，以根据等级一理论的方程来获取其所有爆炸方程。例如，我们明确地给出了三个较高级别的不可用簇，$ -2 $曲线的ADE链和保形物质理论的椭圆爆炸方程。我们还为许多椭圆形的非紧凑型卡拉比（Calabi-Yau）三倍的三倍提供了复合构造，这些椭圆形的构造工程师6d $（1,0）$ scfts具有各种物质表示。
Given the recent geometrical classification of 6d $(1,0)$ SCFTs, a major question is how to compute for this large class their elliptic genera. The latter encode the refined BPS spectrum of the SCFTs, which determines geometric invariants of the associated elliptic non-compact Calabi-Yau threefolds. In this paper we establish for all 6d $(1,0)$ SCFTs in the atomic classification blowup equations that fix these elliptic genera to large extent. The latter fall into two types: the unity- and the vanishing blowup equations. For almost all rank one theories, we find unity blowup equations which determine the elliptic genera completely. We develop several techniques to compute elliptic genera and BPS invariants from the blowup equations, including a recursion formula with respect to the number of strings, a Weyl orbit expansion, a refined BPS expansion and an $ε_1,ε_2$ expansion. For higher-rank theories, we propose a gluing rule to obtain all their blowup equations based on those of rank one theories. For example, we explicitly give the elliptic blowup equations for the three higher-rank non-Higgsable clusters, ADE chain of $-2$ curves and conformal matter theories. We also give the toric construction for many elliptic non-compact Calabi-Yau threefolds which engineer 6d $(1,0)$ SCFTs with various matter representations.
