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Precision microstate counting for the entropy of wrapped M5-branes
Journal of High Energy Physics ( IF 5.4 ) Pub Date : 2020-03-01 , DOI: 10.1007/jhep03(2020)164
Dongmin Gang , Nakwoo Kim , Leopoldo A. Pando Zayas

We study the large N expansion of twisted partition functions of 3d N $$ \mathcal{N} $$ = 2 superconformal field theories arising from N M5-branes wrapped on a hyperbolic 3- manifold, M 3 . Via the 3d-3d correspondence, the partition functions of these 3d N $$ \mathcal{N} $$ = 2 superconformal field theories are related to simple topological invariants on the 3-manifold. The partition functions can be expressed using only classical and one-loop perturbative invariants of PSL( N, ℂ) Chern-Simons theory around irreducible flat connections on M 3 . Using mathematical results on the asymptotics of the invariants, we compute the twisted partition functions in the large N limit including perturbative corrections to all orders in 1 /N . Surprisingly, the perturbative expansion terminates at finite order. The leading part of the partition function is of order N 3 and agrees with the Bekenstein-Hawking entropy of the dual black holes. The subleading part, in particular the log N -terms in the field theory partition function is found to precisely match the one-loop quantum corrections in the dual eleven dimensional supergravity. The field theory results of other terms in 1 /N provide a stringent prediction for higher order corrections in the holographic dual, which is M-theory.

中文翻译:

包裹 M5-膜熵的精确微态计数

我们研究了 3d N $$ \mathcal{N} $$ = 2 超共形场论的扭曲配分函数的大 N 展开,这些场理论由包裹在双曲 3-流形 M 3 上的 N M5-膜产生。通过 3d-3d 对应,这些 3d N $$ \mathcal{N} $$ = 2 超共形场论的配分函数与 3-流形上的简单拓扑不变量有关。分配函数可以仅使用 PSL( N, ℂ) Chern-Simons 理论的经典和单环微扰不变量来表示,该理论围绕 M 3 上的不可约平面连接。使用不变量渐近的数学结果,我们计算大 N 限制中的扭曲分配函数,包括对 1 /N 中所有阶的微扰校正。令人惊讶的是,微扰扩展以有限阶终止。配分函数的前导部分为 N 3 阶,与双黑洞的 Bekenstein-Hawking 熵一致。子引导部分,特别是场论配分函数中的 log N 项被发现与双十一维超引力中的单环量子校正精确匹配。1 /N 中其他项的场论结果为全息对偶中的高阶校正提供了严格的预测,即 M 理论。
更新日期:2020-03-01
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