Matrix integrals & finite holography

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.

Automated summary

The conjectured duality between multicritical matrix integrals (MMI) and a series of non-unitary minimal models was explored, matching critical exponents and revealing novel combinatorial expressions. The finiteness of the continuum theory was elaborated with consideration of BRST cohomology and supported by matrix integrals.