论文标题
在手性环量子量子超级重力中朝向黑洞熵
Towards black hole entropy in chiral loop quantum supergravity
论文作者
论文摘要
最近，已经遇到和澄清了$ \ Mathcal {n} $的许多几何方面 - 延长手性变量中的超级广告。特别是，如果该理论在SUSY转换下也应该在边界上不变，则边界术语必须是$ \ Mathrm {osp}（\ Mathcal {n} | 2）_ {\ Mathbb {C}} $ Super Chern-Simons理论，并且必须满足特定边界条件的作用。基于此，我们提出了一种计算表面熵$ s $的方法，大概包括黑洞透明，在最小情况下的loop量子重力的超对称版本中，$ \ mathcal {n} = 1 $。它类似于非对称理论，通过计算超级切尔 - 西蒙斯理论的量子态空间的尺寸，用于刺穿的固定量子（超级）面积。我们发现大面积的$ s = a_h/4 $，并确定转向校正。由于$ \ mathrm {osp}（1 | 2）_ {\ mathbb {c}} $的非紧密度，以及Chern-Simons量子理论的相应困难，我们使用Verlinde的分析延续，用于compact compact compact compact compact compact compact compact compact compact compact compact compact of compact compact to n ichrm {uosp {uosp {uosp {uosp} $ abaligy n y agib y y y for n y y for。这还需要研究$ \ mathrm {osp}（1 | 2）_ {\ mathbb {c}} $表示的某些属性，我们在文献中没有找到其他地方。
Recently, many geometric aspects of $\mathcal{N}$-extended AdS supergravity in chiral variables have been encountered and clarified. In particular, if the theory is supposed to be invariant under SUSY transformations also on boundaries, the boundary term has to be the action of a $\mathrm{OSp}(\mathcal{N}|2)_{\mathbb{C}}$ super Chern-Simons theory, and particular boundary conditions must be met. Based on this, we propose a way to calculate an entropy $S$ for surfaces, presumably including black hole horizons, in the supersymmetric version of loop quantum gravity for the minimal case $\mathcal{N}=1$. It proceeds in analogy to the non-supersymmetric theory, by calculating dimensions of quantum state spaces of the super Chern-Simons theory with punctures, for fixed quantum (super) area of the surface. We find $S = a_H/4$ for large areas and determine the subleading correction. Due to the non-compactness of $\mathrm{OSp}(1|2)_{\mathbb{C}}$ and the corresponding difficulties with the Chern-Simons quantum theory, we use analytic continuation from the Verlinde formula for a compact real form, $\mathrm{UOSp}(1|2)$, in analogy to work by Noui et al. This also entails studying some properties of $\mathrm{OSp}(1|2)_{\mathbb{C}}$ representations that we have not found elsewhere in the literature.
