Gravitational description of the conformally invariant quantum mechanics of large matrices
Hanmer, Jeffrey Thomas
We study the collective field theory of a free multi-matrix model in the radial sector, which has an emergent 1/r2 term, and take the large N limit. We show that it is possible to generate 2−d metrics with generic dependence on the collective field Lagrange multiplier (μ) and potential and which are distinguished by the choice of the potential. The Lagrange multiplier is shown to depend on an induced scale parameter after an I.R. regularization and breaks scale invariance. The collective field sl(2, R) algebras of the free Hamiltonian and a related alternative compact operator only close in the absence of μ. We point out that the broken conformal symmetry is contained in the associated metrics which suggests that they are related to a Near-AdS2 geometry. We also comment on the resemblance of these metrics to black hole solutions.
A dissertation submitted to the faculty of science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science. July 6, 2017.
Hanmer, Jeffrey Thomas (2017) Gravitational description of the conformally invariant quantum mechanics of large matrices, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/24176>