arXiv 2203.066292022-03hep-th

关于$(2,2p+1)$极小Liouville引力和模空间体积的大$p$极限的注记

Note on large-$p$ limit of $(2,2p+1)$ minimal Liouville gravity and moduli space volumes

Aleksandr Artemev

备注：: 13 pages; added references and minor corrections, matches version published in NPB
发表信息：: Nuclear Physics B, Volume 981, August 2022, 115876
DOI：: 10.1016/j.nuclphysb.2022.115876

摘要：

本文研究了二维Liouville引力场与$(2,2p+1)$极小模型耦合的关联数在大$p$上的一些性质。在极限$p \to \infty$，对于一些明确已知的例子，在一个特定的区域的参数空间的相关数示出，以减少到威尔-彼得森体积，解析继续虚测地线长度。这标志着这个极限与JT引力的另一个联系。我们还评论了假设的几何意义，得到的答案以外的这个区域，特别是，的含义的极小模型融合规则。另一个观察是当与相关器的参数相比，$p$足够大时，相关数与共形块的数量成比例。即使不取极限，这种比例也是有效的。

英文摘要：

In this note we report on some properties of correlation numbers for 2-dimensional Liouville gravity coupled with $(2,2p+1)$ minimal model at large $p$. In the limit $p \to \infty$, for some explicitly known examples in a particular region of parameter space correlation numbers are shown to reduce to Weil-Petersson volumes, analytically continued to imaginary geodesic lengths. This marks another connection of this limit with JT-gravity. We also comment on supposed geometric meaning of the obtained answers outside of this region, in particular, the meaning of the minimal model fusion rules. Another observation is the proportionality of correlation number to the number of conformal blocks when $p$ is big enough compared to parameters of the correlator. This proportionality is valid even without taking the limit.

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