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 Bogomol’nyi-Prasad-Sommerfield (BPS) states in this setting correspond to M2-branes stretched between the M5-branes. Generalizing an observation made by Ahmed et al. [Bound states of little strings and symmetric orbifold conformal field theories, Phys. Rev. D 96, 081901 (2017).], 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 neighboring 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 conformal field theories. We show, furthermore, that to leading instanton order (in the NS limit) the reduced BPS counting functions factorize 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.

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来自少量弦残留物的对称球对称理论

我们研究了一类A型的小字符串理论（LST），由 $ñ$ 平行的M5球散布成一个圆，在低能态下，工程师设计了超对称轨距理论， $ü（ñ）$仪表组。此设置中的Bogomol'nyi-Prasad-Sommerfield（BPS）状态对应于在M5大脑之间伸展的M2大脑。概括了艾哈迈德（Ahmed）等人的观察。[小弦的束缚态和对称双共形共形场理论，物理学。启d 96，081901（2017）]中，我们提供了证据，后者表现出的特殊分部门的BPS计数功能的赫克结构在涅克拉索夫-Shatashvili（NS）的限制。; 也就是说，超对称规范理论在瞬时扩展中的不同阶数是通过Hecke算子的作用来关联的。我们提取$ñ$ 借助轮廓积分相对于LST的量规参数，与LST的全部自由能截然不同的这种减少的BPS计数功能 $ü（ñ）$仪表组。从物理上讲，这些功能捕获的状态对应于以下配置：在这些相邻的M5-大脑中的某些之间伸展相同数量的M2-大脑，而其余的M5-大脑彼此折叠，并提取特定的奇异贡献。Hecke结构表明，这些BPS状态形成了对称双峰共形场理论的谱。此外，我们表明，领先的瞬时顺序（在NS限制内），减少的BPS计数功能可分解为更简单的构造块。这些构成要素是自由能的膨胀系数$ñ=\mathrm{1个}$以及扩展特定功能的功能，该功能控制单个M5-branes两端都带有单个M2-branes的BPS状态的计数。对于瞬时展开的更高阶，我们观察到在此分解中出现的新元素，它们的系数通过全纯异常方程式相关。