Statistical physics of the polarised IKKT matrix model

The polarised IKKT matrix model is the worldpoint theory of N N D-instantons in a background three-form flux of magnitude \Omega Ω , and promises to be a highly tractable model of holography. The matrix integral can be viewed as a statistical physics partition function with inverse temperature \Omega^4 Ω 4 . At large \Omega Ω the model is dominated by a matrix configuration corresponding to a ‘polarised’ spherical D1-brane. We show that at a critical value of \Omega^2 N Ω 2 N the model undergoes a first order phase transition, corresponding to tunneling into a collection of well-separated D-instantons. These instantons are the remnant of a competing saddle in the high \Omega Ω phase corresponding to spherical (p,q) ( p , q ) fivebranes. We use a combination of numerical and analytical arguments to capture the different regimes of the model.