arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新，休息一下吧，周末愉快~~
arXiv 1609.02558hep-th
收藏

$\mathrm{AdS}_4\times S^7/\mathbb{Z}_k$上的单圈超引力及其与ABJM理论的比较

One-loop supergravity on $\mathrm{AdS}_4\times S^7/\mathbb{Z}_k$ and comparison with ABJM theory

James T. Liu, Wenli Zhao

备注：
22 pages, 1 figure, discussion on the O(N^{1/2}) order and references added
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

ABJM理论的大$N$极限与AdS $_4\times S^7/\mathbb{Z}_k$上的M理论是全息对偶的。通过定域化得到了3球配分函数，其主导行为$F_{\text{ABJM}}^{(0)}\sim k^{1/2}N^{3/2}$在树级超引力的对偶理论中得到了精确的再现。我们通过计算作为$k$的函数的单圈超引力自由能并将其与ABJM结果进行比较，将这种比较扩展到次领先的$\mathcal O(N^0)$阶。奇怪的是，我们发现表达式不匹配，与$F_{\text{SUGRA}}^{(1)}\sim k^6$，而$F_{\text{ABJM}}^{(1)}\sim k^2$。这表明低能近似$Z_{\text{M-theory}}=Z_{\text{SUGRA}}$在单圈阶下失效。

英文摘要：

The large-$N$ limit of ABJM theory is holographically dual to M-theory on AdS$_4\times S^7/\mathbb{Z}_k$. The 3-sphere partition function has been obtained via localization, and its leading behavior $F_{\text{ABJM}}^{(0)}\sim k^{1/2}N^{3/2}$ is exactly reproduced in the dual theory by tree-level supergravity. We extend this comparison to the sub-leading $\mathcal O(N^0)$ order by computing the one-loop supergravity free energy as a function of $k$ and comparing it with the ABJM result. Curiously, we find that the expressions do not match, with $F_{\text{SUGRA}}^{(1)}\sim k^6$, while $F_{\text{ABJM}}^{(1)}\sim k^2$. This suggests that the low-energy approximation $Z_{\text{M-theory}}=Z_{\text{SUGRA}}$ breaks down at one-loop order.

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。

↑