论文标题
Chern-Simons理论与特殊量规组作为精制拓扑弦
Chern-Simons theory with the exceptional gauge group as a refined topological string
论文作者
论文摘要
我们以三个球员的形式在三个球体上以划分的闭合拓扑字符串的形式呈现了Chern-Simons理论的分区函数，并在单个封闭式拓扑字符串的划分函数的形式中，$2τ= g_s（1-b）$（1-b）$ $ b = \ frac {5} {3}，\ frac {5} {2}，3,4,6 $，分别为$ g_2，f_4，e_6，e_6，e_7，e_8 $。非零BPS不变性$ n^d_ {J_l，J_R} $（$ D $ - 度）为$ n^2_ {0，\ frac {1} {2}} = 1，n^{11} _ {11} _ {0,1} = 1 $。除这些术语外，Chern-Simons理论的分区功能还包含与弦理论的精制恒定图相对应的术语。 推导基于Chern-Simons分区功能的通用（从Vogel的意义上）基于三个球体的chern-simons分区函数，仅限于特殊的线$ exc $，其中vogel的参数满足$γ= 2（α+β）$。该线包含对应于所有特殊组的点。对于$ f $ line $γ=α+β$（包含$ su（4），so（10）$和$ e_6 $组），获得了相同的结果，其中non-Zero $ n^2_ {0，\ frac {1} {1} {2} {2} {2}} = 1，n^{7} _ {7} _ {0} _ {0,1} = 1 $ $ $。 在这两种情况下，细化参数$ b $（$ = - ε_2/ε_1$在Nekrasov的参数方面）都是通过通用参数给出的，仅限于该行，由$ b =-β/α$。
We present the partition function of Chern-Simons theory with the exceptional gauge group on three-sphere in the form of a partition function of the refined closed topological string with relation $2τ=g_s(1-b) $ between single Kähler parameter $τ$, string coupling constant $g_s$ and refinement parameter $b$, where $b=\frac{5}{3},\frac{5}{2},3,4,6$ for $G_2, F_4, E_6, E_7, E_8$, respectively. The non-zero BPS invariants $N^d_{J_L,J_R}$ ($d$ - degree) are $N^2_{0,\frac{1}{2}}=1, N^{11}_{0,1}=1$. Besides these terms, partition function of Chern-Simons theory contains term corresponding to the refined constant maps of string theory. Derivation is based on the universal (in Vogel's sense) form of a Chern-Simons partition function on three-sphere, restricted to exceptional line $Exc$ with Vogel's parameters satisfying $γ=2(α+β)$. This line contains points, corresponding to the all exceptional groups. The same results are obtained for $F$ line $γ=α+β$ (containing $SU(4), SO(10)$ and $E_6$ groups), with the non-zero $N^2_{0,\frac{1}{2}}=1, N^{7}_{0,1}=1$. In both cases refinement parameter $b$ ($=-ε_2/ε_1$ in terms of Nekrasov's parameters) is given in terms of universal parameters, restricted to the line, by $b=-β/α$.
