arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.05213hep-th
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M-膜指数的有限- $N$修正

Finite-$N$ corrections to the M-brane indices

Reona Arai, Shota Fujiwara, Yosuke Imamura, Tatsuya Mori, Daisuke Yokoyama

摘要:

我们研究了有限$N$修正M2-和M5-膜上实现的理论的超共形指数。对于在$N$ M2-膜的堆叠上实现的三维理论,我们计算有限的$N$修正作为扩展的M5-膜在对偶几何$AdS_4\times \boldsymbol{S}^7$中的贡献。我们只考虑了具有单缠绕的M5-膜构型,而忽略了多缠绕构型。我们比较的结果与从ABJM理论计算的指数,并发现协议预期的错误,由于多重包装。对于$N$ M5-膜的六维理论,我们通过分析$AdS_7\times \boldsymbol{S}^4$中的扩展M2-膜来计算指数。同样,我们只包括具有单包装的配置。我们首先将$N=1$的结果与自由张量多重态的索引进行比较,以估计由于多重缠绕而导致的误差的阶数。我们计算了$A_{N-1}$理论的指数的前几项,并确认它们可以通过超共形表示展开。我们还讨论了多重包裹的贡献,六维舒尔样指数。

英文摘要:

We investigate finite-$N$ corrections to the superconformal indices of the theories realized on M2- and M5-branes. For three-dimensional theories realized on a stack of $N$ M2-branes we calculate the finite-$N$ corrections as the contribution of extended M5-branes in the dual geometry $AdS_4\times \boldsymbol{S}^7$. We take only M5-brane configurations with a single wrapping into account, and neglect multiple-wrapping configurations. We compare the results with the indices calculated from the ABJM theory, and find agreement up to expected errors due to the multiple wrapping. For six-dimensional theories on $N$ M5-branes we calculate the indices by analyzing extended M2-branes in $AdS_7\times \boldsymbol{S}^4$. Again, we include only configurations with single wrapping. We first compare the result for $N=1$ with the index of the free tensor multiplet to estimate the order of the error due to multiple wrapping. We calculate first few terms of the index of $A_{N-1}$ theories explicitly, and confirm that they can be expanded by superconformal representations. We also discuss multiple-wrapping contributions to the six-dimensional Schur-like index.

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