High Temperature Limit of the N= 2 Matrix Model

We consider a system of D0-branes in toroidally compactified space with interactions described by a Born-Infeld-type generalisation of the leading v^2 + v^4/r^{D-4} terms (D is the number of non-compact directions in M-theory, including the longitudinal one). This non-linear action can be interpreted as an all-loop large N super Yang-Mills effective action and has a remarkable scaling property. We first study the classical dynamics of a brane probe in the field of a central b...

We calculate the high-temperature expansion of the 2-point function up to order 800 in beta. We show that estimations of the critical exponent gamma based on asymptotic analysis are not very accurate in presence of confluent logarithmic singularities. Using a direct comparison between the actual series and the series obtained from a parametrization of the form (beta_c -beta)^(-gamma) (Ln(beta_c -beta))^p +r), we show that the errors are minimized for gamma =0.9997 and p=0.335...

Spinning black three-branes in type IIB supergravity are thermodynamically stable up to a critical value of the angular momentum density. Inside the region of thermodynamic stability, the free energy from supergravity is roughly reproduced by a naive model based on free N=4 super-Yang-Mills theory on the world-volume. The field theory model correctly predicts a limit on angular momentum density, but near this limit it does not reproduce the critical exponents one can compute ...

We perform two independent calculations of the two-loop partition function for the large N 't Hooft limit of the plane-wave matrix model, conjectured to be dual to the decoupled little string theory of a single spherical type IIA NS5-brane. The first is via a direct two-loop path-integral calculation in the matrix model, while the second employs the one-loop dilatation operator of four-dimensional N = 4 Yang-Mills theory truncated to the SU(2|4) subsector. We find precise agr...

We propose a useful integral representation of the quenched free energy which is applicable to any random systems. Our formula involves the generating function of multi-boundary correlators, which can be interpreted on the bulk gravity side as spacetime D-branes introduced by Marolf and Maxfield in [arXiv:2002.08950]. As an example, we apply our formalism to the Airy limit of the random matrix model and compute its quenched free energy under certain approximations of the gene...

Various aspects of branes in the recently proposed matrix model for M theory are discussed. A careful analysis of the supersymmetry algebra of the matrix model uncovers some central charges which can be activated only in the large $N$ limit. We identify the states with non-zero charges as branes of different dimensions.

We study real time classical matrix mechanics of a simplified $2\times 2$ matrix model inspired by the black hole evaporation problem. This is a step towards making a quantitative model of real time evaporation of a black hole, which is realized as a bound state of D0-branes in string theory. The model we study is the reduction of Yang Mills in $2+1$ dimension to $0+1$ dimensions, which has been corrected with an additional potential that can be interpreted as a zero point en...

Some recent work on the thermodynamic behavior of the matrix model of M-theory on a pp-wave background is reviewed. We examine a weak coupling limit where computations can be done explicitly. In the large N limit, we find a phase transition between two distinct phases which resembles a ``confinement-deconfinement'' transition in gauge theory and which we speculate must be related to a geometric transition in M-theory. We review arguments that the phase transition is also rela...

Multi-loop calculations of the effective action for the matrix model are important for carrying out tests of the conjectured relationship of the matrix model to the low energy description of M-theory. In particular, comparison with N-graviton scattering amplitudes in eleven-dimensional supergravity requires the calculation of the effective action for the matrix model with gauge group SU(N). A framework for carrying out such calculations at two loops is established in this pap...

In the present paper we calculate the statistical partition function for any number of extended objects in Matrix theory in the one loop approximation. As an application, we calculate the statistical properties of K clusters of D0 branes and then the statistical properties of K membranes which are wound on a torus.