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 Yang-Mills-to-fuzzy-sphere phase where the fuzzy sphere solution is only manifested as a three-cut configuration termed the "baby fuzzy sphere" configuration. The Yang-Mills 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 semi-circle law, and ii) the uniform distribution at small values of the temperatures is non-existent.

47 pages, 14 figures

References in corpus (6)

• Geometry in transition: A model of emergent geometry
• Phase structure of matrix quantum mechanics at finite temperature
• High temperature expansion in supersymmetric matrix quantum mechanics
• Five-Brane Thermodynamics from the Matrix Model
• Exact fuzzy sphere thermodynamics in matrix quantum mechanics
• Areas and entropies in BFSS/gravity duality

Cited by in corpus (1)

• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry II: Noncommutative Quantum Black Holes