Two approaches to quantum gravity and M(atrix) theory at large number of dimensions
Abstract
A Gaussian approximation to the bosonic part of M(atrix) theory with mass deformation is considered at large values of the dimension d. From the perspective of the gauge/gravity duality this action reproduces with great accuracy the stringy Hagedorn phase transition from a confinement (black string) phase to a deconfinement (black hole) phase whereas from the perspective of the matrix/geometry approach this action only captures a remnant of the geometric YangMillstofuzzysphere phase where the fuzzy sphere solution is only manifested as a threecut configuration termed the “baby fuzzy sphere” configuration. The YangMills phase retains most of its characteristics with two exceptions: (i) the uniform distribution inside a solid ball suffers a crossover at very small values of the gauge coupling constant to a Wigner’s semicircle law, and (ii) the uniform distribution at small values of the temperatures is nonexistent.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 November 2021
 DOI:
 10.1142/S0217751X21502341
 arXiv:
 arXiv:2007.04488
 Bibcode:
 2021IJMPA..3650234Y
 Keywords:

 Noncommutative geometry;
 matrix models;
 gauge/gravity duality;
 black hole physics;
 emergent geometry;
 fuzzy sphere;
 02.10.Yn;
 02.40.−k;
 02.70.Uu;
 03.70.+k;
 04.50.Gh;
 04.60.−m;
 04.70.−s;
 05.70.Fh;
 11.10.Kk;
 11.10.Lm;
 11.10.Wx;
 11.15.−q;
 11.15.Ha;
 11.15.Pg;
 Matrix theory;
 Applications of Monte Carlo methods;
 Theory of quantized fields;
 Higherdimensional black holes black strings and related objects;
 Phase transitions: general studies;
 Field theories in dimensions other than four;
 Nonlinear or nonlocal theories and models;
 Finitetemperature field theory;
 Lattice gauge theory;
 Expansions for large numbers of components;
 High Energy Physics  Theory
 EPrint:
 47 pages, 14 figures