论文标题
来自小绳子残基的对称轨道理论
Symmetric Orbifold Theories from Little String Residues
论文作者
论文摘要
我们研究了一种类型的小弦理论（LST），由$ n $平行的M5-branes散布在圆圈上，在低能制度工程师的超级对称规格中，它们具有$ u（n）$ gauge group。 BPS在此设置中的状态对应于M5-贿赂之间伸展的M2晶体。 Generalising an observation made in arXiv:1706.04425, we provide evidence that the BPS counting functions of special subsectors of the latter exhibit a Hecke structure in the Nekrasov-Shatashvili (NS) limit, i.e. the different orders in an instanton expansion of the supersymmetric gauge theory are related through the action of Hecke operators.我们从LST的全部自由能中提取$ n $ distions降低的BPS计数功能，借助轮廓积分，就$ u（n）$量规组的量规参数而言。从物理上讲，这些功能捕获的状态对应于这些相邻的M5-branes之间伸展相同数量的M2-branes的配置，而其余的M5-Branes彼此之间崩溃并提取了特定的单数贡献。 Hecke结构表明，这些BPS状态形成了对称Orbifold CFT的光谱。我们进一步表明，要领导instanton Order（在NS-LIMIT中），将降低的BPS计数函数分解为更简单的构建块。这些构建块是自由能的扩展系数，$ n = 1 $，并且是特定功能的扩展，该功能控制了单个M5-Brane的BPS状态，单个M2-branes在任一侧都以单个M2-Branes结束。对于intsanton扩展中的较高阶，我们观察到了这种分解中出现的新元素，其系数通过全体形态异常方程相关。
We study a class of Little String Theories (LSTs) of A type, described by $N$ parallel M5-branes spread out on a circle and which in the low energy regime engineer supersymmetric gauge theories with $U(N)$ gauge group. The BPS states in this setting correspond to M2-branes stretched between the M5-branes. Generalising an observation made in arXiv:1706.04425, we provide evidence that the BPS counting functions of special subsectors of the latter exhibit a Hecke structure in the Nekrasov-Shatashvili (NS) limit, i.e. the different orders in an instanton expansion of the supersymmetric gauge theory are related through the action of Hecke operators. We extract $N$ distinct such reduced BPS counting functions from the full free energy of the LST with the help of contour integrals with respect to the gauge parameters of the $U(N)$ gauge group. Physically, the states captured by these functions correspond to configurations where the same number of M2-branes is stretched between some of these neighbouring M5-branes, while the remaining M5-branes are collapsed on top of each other and a particular singular contribution is extracted. The Hecke structures suggest that these BPS states form the spectra of symmetric orbifold CFTs. We furthermore show that to leading instanton order (in the NS-limit) the reduced BPS counting functions factorise into simpler building blocks. These building blocks are the expansion coefficients of the free energy for $N=1$ and the expansion of a particular function, which governs the counting of BPS states of a single M5-brane with single M2-branes ending on it on either side. To higher orders in the instanton expansion, we observe new elements appearing in this decomposition, whose coefficients are related through a holomorphic anomaly equation.
