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arXiv 1902.09504hep-th
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纯旋量超弦中隐藏的特殊对称性

Hidden exceptional symmetry in the pure spinor superstring

Richard Eager, Guglielmo Lockhart, Eric Sharpe

备注：
8 pages, 1 figure; v2: added references, minor updates
发表信息：
Phys. Rev. D 101, 026006 (2020)
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摘要：

超弦理论的纯旋量表述包括中心电荷$c_λ=22$的相互作用扇区，它可以被实现为正交格拉斯曼$\text{OG}^{+}(5,10)$上的圆锥上的弯曲$βγ$系统。我们发现，$βγ$系统的频谱组织成表示的$\mathfrak{g}=\mathfrak{e}_6$仿射代数在$-3$水平，其$\mathfrak{so}(10)_{-3}\oplus {\mathfrak u}(1)_{-4}$子代数编码的旋转和鬼对称的系统。因此，纯旋量配分函数分解为仿射$\mathfrak{e}_6$特征的和。我们将其解释为弯曲$βγ$系统中更普遍的增强模式的实例，该系统还包括$\mathfrak{g}=\mathfrak{so}(8)$和$\mathfrak{e}_7$的情况，对应于在复格拉斯曼$\text{Gr}(2,4)$和复凯莱平面$\mathbb{OP}^2$上的锥的目标空间。我们确定这些弯曲的$βγ$系统的手征代数的某些$2d$ $(0,2)$ CFTs所产生的扭曲紧化的4D $\mathcal{N}=2$ SCFTs的$S^2$。

英文摘要：

The pure spinor formulation of superstring theory includes an interacting sector of central charge $c_λ=22$, which can be realized as a curved $βγ$ system on the cone over the orthogonal Grassmannian $\text{OG}^{+}(5,10)$. We find that the spectrum of the $βγ$ system organizes into representations of the $\mathfrak{g}=\mathfrak{e}_6$ affine algebra at level $-3$, whose $\mathfrak{so}(10)_{-3}\oplus {\mathfrak u}(1)_{-4}$ subalgebra encodes the rotational and ghost symmetries of the system. As a consequence, the pure spinor partition function decomposes as a sum of affine $\mathfrak{e}_6$ characters. We interpret this as an instance of a more general pattern of enhancements in curved $βγ$ systems, which also includes the cases $\mathfrak{g}=\mathfrak{so}(8)$ and $\mathfrak{e}_7$, corresponding to target spaces that are cones over the complex Grassmannian $\text{Gr}(2,4)$ and the complex Cayley plane $\mathbb{OP}^2$. We identify these curved $βγ$ systems with the chiral algebras of certain $2d$ $(0,2)$ CFTs arising from twisted compactification of 4d $\mathcal{N}=2$ SCFTs on $S^2$.

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