How to Build a Black Hole out of Instantons


An often fruitful route to study quantum gravity is the determination and study of quantum mechanical models–that is, models with finite degrees of freedom–that capture the dynamics of a black hole’s microstates. An example of such a model is the superconformal quantum mechanics of Yang-Mills instantons, which has a proposed gravitational dual description as M-theory on a background of the form $X_7\times S^4$. This model arises in the strongly-coupled limit of the BFSS matrix model with additional fundamental hypermultiplets, offering a route towards useful numerical simulation. We construct a six-parameter black hole solution in this theory, which is generically non-supersymmetric and non-extremal, and is shown to arise in an “ultra-spinning'' limit of the recently-found six-parameter AdS$_7$ solution. We compute its thermodynamic properties, and show that in the supersymmetric limit the entropy and on-shell action match precisely the expected results as computed from the superconformal index of the quantum mechanics, to leading order in the supergravity regime. The low-lying spectrum thus provides access to the dynamics of near-extremal black holes, whose spectra are expected to receive strong quantum corrections.

Rishi Mouland
Rishi Mouland
Research Associate in High Energy Theoretical Physics

My research interests include string theory, M-theory and conformal field theory