Half-wormholes in SYK with one time point
Half-wormholes in SYK with one time point
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DOI：
10.21468/scipostphys.12.1.029
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发表时间：
2021-05
期刊：
影响因子：
5.5
通讯作者：
Baur Mukhametzhanov
中科院分区：
文献类型：
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作者：
Baur Mukhametzhanov
在这篇笔记中，我们研究了带有一个时间点的SYK模型，最近Saad，Shenker，Stanford和姚考虑了这一模型。在集体的场描述中，他们得出了一个非凡的恒等式：具有固定耦合的配分函数的平方很好地近似为“虫洞”鞍加“一对相连的半虫洞”鞍形。它解释了解耦系统的因式分解。在这里，我们得到了半虫洞贡献的一个显式公式。它是通过SYK耦合张量的超法夫函数来表示的。然后我们在半虫洞鞍座周围展开微扰展开。这个展开式在有限阶处截断，并给出了准确的答案。微扰展开中的最后一项与虫洞的贡献相吻合。在这个意义上，这个模型中的虫洞鞍点不需要单独添加，而是可以被视为连接的半个虫洞周围的一个巨大的波动。
In this note we study the SYK model with one time point, recently considered by Saad, Shenker, Stanford, and Yao. Working in a collective field description, they derived a remarkable identity: the square of the partition function with fixed couplings is well approximated by a ``wormhole'' saddle plus a ``pair of linked half-wormholes'' saddle. It explains factorization of decoupled systems. Here, we derive an explicit formula for the half-wormhole contribution. It is expressed through a hyperpfaffian of the tensor of SYK couplings. We then develop a perturbative expansion around the half-wormhole saddle. This expansion truncates at a finite order and gives the exact answer. The last term in the perturbative expansion turns out to coincide with the wormhole contribution. In this sense the wormhole saddle in this model does not need to be added separately, but instead can be viewed as a large fluctuation around the linked half-wormholes.