Journal of High Energy Physics (Jun 2021)

Matrix integrals & finite holography

  • Dionysios Anninos,
  • Beatrix Mühlmann

Journal volume & issue
Vol. 2021, no. 6
pp. 1 – 50


Read online

Abstract 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.