发表机构
Klaviyo（Klaviyo）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
三维加一维拓扑超导体边界带Z₁₆全局反常，最小超对称标准模型因引力微子贡献问题阻碍Z₄规范，该研究发现四维N=8超引力的费米子可饱和该反常，使Z₄保持无反常且可规范，源于Smith同态将超引力反常与拓扑超导体反常等同。
AI 中文摘要
三维加一维（$3{+}1$）拓扑超导体的边界带有取值为$\boldsymbol{\textit{Z}_{16}}$的全局（Dai-Freed）反常，在对特定$\boldsymbol{\textit{Z}_4}$对称性进行规范后，标准模型一代的16个费米子可实现该反常的匹配。不过在超引力完备化中，引力微子贡献$-7/16$而非$\boldsymbol{\textit{\textpm}1/16}$，这会阻碍最小超对称标准模型中的$\boldsymbol{\textit{Z}_4}$。我们发现四维$\boldsymbol{\textit{N}=8}$超引力可避免这一问题：其费米子包括$\boldsymbol{8}$表示中的8个引力微子，以及$\boldsymbol{SU(8)}$ R对称性的$\boldsymbol{\textit{56}=\boldsymbol{\textit{\textLambda}^3\boldsymbol{8}}$表示中的56个自旋-$1/2$态，这些费米子可使反常饱和。该抵消对所有可允许的$\boldsymbol{\textit{Z}_4}$结构均成立，与连续$\boldsymbol{SU(8)}$反常的消失一致，且源于将超引力反常与拓扑超导体反常等同的Smith同态。在最大超引力中，尽管存在8个引力微子，该$\boldsymbol{\textit{Z}_4}$仍保持无反常且可规范，所有数值均可通过补充材料中描述的开源库复现。
英文摘要
The boundary of a $3{+}1$-dimensional topological superconductor carries a $\mathbb{Z}_{16}$-valued global (Dai-Freed) anomaly, famously matched by the $16$ fermions of a Standard Model generation once a certain $\mathbb{Z}_4$ symmetry is gauged. In a supergravity completion, though, a gravitino contributes $-7/16$ rather than $\pm1/16$, obstructing this $\mathbb{Z}_4$ in the Minimal Supersymmetric Standard Model. We observe that four-dimensional $\mathcal{N}=8$ supergravity evades this fate. Its fermions, eight gravitini in the $\mathbf 8$ and fifty-six spin-$\tfrac12$ states in the $\mathbf{56}=Λ^3\mathbf 8$ of the $SU(8)$ R-symmetry, cancel the anomaly. The cancellation holds for every admissible $\mathbb{Z}_4$ structure, is consistent with the vanishing of the continuous $SU(8)$ anomaly, and follows from a Smith homomorphism and the Rarita-Schwinger ghost-subtraction weight identifying the supergravity anomaly with that of the topological superconductor. In maximal supergravity this $\mathbb{Z}_4$ stays anomaly-free and gaugeable despite its eight gravitini. All numbers are reproduced by an open-source library described in the Supplemental Material.
Comments4 pages + 1 page supplemental material, 1 figure, 1 table; v2 - 1 reference and corresponding discussion added
