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arXiv 2310.03332hep-th
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环面与定向折的简单和巨引力子展开

Simple-Sum Giant Graviton Expansions for Orbifolds and Orientifolds

Shota Fujiwara, Yosuke Imamura, Tatsuya Mori, Shuichi Murayama, Daisuke Yokoyama

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66 pages, 23 figures, v2: references added, v3: minor corrections
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AI总结：

本文研究四维环面/定向折理论的巨引力子展开，发现特定例子可简化为简单求和，并论证该简化仅当Calabi-Yau为三角形环面图时成立。

摘要：

我们研究了四维环面/定向折理论的超共形指标的巨引力子展开。一般而言，巨引力子展开是环绕数的多重求和。已知对于${\cal N}=4$ $U(N)$ SYM，通过选择合适的展开变量，该展开可以简化为简单求和。我们发现对于环面和定向折理论的几个例子，即$\mathbb{Z}_k$环面和具有$O3$与$O7$的定向折，这种简化确实发生。我们还论证了，对于与环面Calabi-Yau三维流形相关的箭袋规范理论，简单求和展开仅在环面图为三角形时成立，即该Calabi-Yau是$\mathbb{C}^3$的环面折。

英文摘要：

We study giant graviton expansions of the superconformal index of 4d orbifold/orientifold theories. In general, a giant graviton expansion is given as a multiple sum over wrapping numbers. It has been known that the expansion can be reduced to a simple sum for the ${\cal N}=4$ $U(N)$ SYM by choosing appropriate expansion variables. We find such a reduction occurs for a few examples of orbifold and orientifold theories: $\mathbb{Z}_k$ orbifold and orientifolds with $O3$ and $O7$. We also argue that for a quiver gauge theory associated with a toric Calabi-Yau $3$-fold the simple-sum expansion works only if the toric diagram is a triangle, that is, the Calabi-Yau is an orbifold of $\mathbb{C}^3$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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