论文标题
矩阵积分$ \＆$有限全息图
Matrix integrals $\&$ finite holography
论文作者
论文摘要
我们探讨了一类大的$ n $矩阵积分（称为多政治矩阵积分（MMI））与在波动背景下的非独立最小模型的系列二元性。我们将MMI领先订单平面扩展的关键指数与关于$ S^2 $拓扑的连续性理论的关键指数相匹配。从MMI的角度来看，这既可以通过多Vertex图形扩展来完成，从而揭示了新型的组合表达式，以及通过对矩阵积分作为其参数的函数的系统鞍点评估。从连续的角度来看，在存在给定的共形初级的情况下计算分区函数时，可以获得相应的临界指数。除此之外，我们详细介绍了连续理论的希尔伯特空间及其推定的有限性，均在$ s^2 $和$ t^2 $拓扑的情况下使用BRST共同体学考虑。矩阵积分支持这种有限。
We explore the conjectured duality between a class of large $N$ matrix integrals, known as multicritical matrix integrals (MMI), and the series $(2m-1,2)$ of non-unitary minimal models on a fluctuating background. We match the critical exponents of the leading order planar expansion of MMI, to those of the continuum theory on an $S^2$ topology. From the MMI perspective this is done both through a multi-vertex diagrammatic expansion, thereby revealing novel combinatorial expressions, as well as through a systematic saddle point evaluation of the matrix integral as a function of its parameters. From the continuum point of view the corresponding critical exponents are obtained upon computing the partition function in the presence of a given conformal primary. Further to this, we elaborate on a Hilbert space of the continuum theory, and the putative finiteness thereof, on both an $S^2$ and a $T^2$ topology using BRST cohomology considerations. Matrix integrals support this finiteness.
