论文标题
3D超符号指数和对双黑洞熵的矫正
Cardy Expansion of 3d Superconformal Indices and Corrections to the Dual Black Hole Entropy
论文作者
论文摘要
我们考虑三维$ {\ cal n} = 2 $超对称字段理论通过$ s^1 \ times s^2 $计算的超级符号索引。我们系统地发展了一个扩展，其中$ s^1 $与$ s^2 $的半径的比率非常小 - 类似于性基的扩展。我们强调了这种类似Cardy的扩展中的子领导结构，以及与$ U（n）$因子的表单产品量规组的较大$ n $限制的相互作用。我们证明，将大的$ n $限制首先导致该索引的表达式，该索引仅包含与$ 1/β$成比例的术语和$β^{i = 0,1,2} $的功率，其中$β$是半径的比例。当我们从有限$ n $的$β\到0 $限制时，我们发现了$ e^{ - 1/β} $的非扰动贡献的指示。对于ABJM理论，我们探讨了类似Cardy的扩展对校正对旋转，电动充电，渐近广告$ _4 $双重黑洞的熵的含义。有趣的是，我们发现，$β$中的校正可以通过适当移动电荷和角动量来解释熵
We consider the superconformal index of three-dimensional ${\cal N}=2$ supersymmetric field theories computed via localization on $S^1\times S^2$. We systematically develop an expansion where the ratio of the radius of $S^1$ to the radius of $S^2$ is taken very small -- a Cardy-like expansion. We emphasize the sub-leading structures in this Cardy-like expansion as well as their interplay with the large-$N$ limit for theories with gauge group of the form product of $U(N)$ factors. We demonstrate that taking the large-$N$ limit first leads to an expression for the index that only includes terms proportional to $1/β$ and powers of $β^{i=0,1,2}$ where $β$ is the ratio of radii. As we depart from the $β\to 0$ limit for finite $N$, we find indications of non-perturbative contributions of the form $e^{-1/β}$. For the ABJM theory we explore the implications of the Cardy-like expansion for corrections to the entropy of the rotating, electricallly charged, asymptotically AdS$_4$ dual black hole. Interestingly, we find that the corrections in $β$ to the entropy can be accounted for by appropriately shifting the electric charges and the angular momentum
