Phases of one dimensional large N gauge theory in a 1/D expansion

Abstract

We consider large N Yang Mills theory with D adjoint scalar fields in d dimensions for d = 0 or 1. We show the existence of a non-trivial saddle point of the functional integral at large D which is characterized by a mass gap for the adjoint scalars. We integrate out the adjoint scalars in a 1/D expansion around the saddle point. In case of one dimension which is regarded as a circle, this procedure leads to an effective action for the Wilson line. We find an analogue of the confinement/deconfinement transition which consists of a second order phase transition from a uniform to a non-uniform eigenvalue distribution of the Wilson line, closely followed by a Gross-Witten-Wadia transition where a gap develops in the eigenvalue distribution. The phase transition can be regarded as a continuation of a Gregory-Laflamme transition. Our methods involve large values of the dimensionless 'tHooft coupling. The analysis in this paper is quantitatively supported by earlier numerical work for D = 9.

The BFSS model on the lattice

“…The model has been studied already both theoretically [8] (see also ref. [9]) and numerically [10,11] and our results are in accord with these studies. The zero temperature supersymmetric gauge theory has been studied in a hamiltonian light cone context in ref.…”

“…Surprisingly this model knows lots about the phase transition of the full model. An analysis similar to that above shows that the critical temperature for p adjoint gauged Gaussian matrices as in [9] with mass m occurs at T Gaussian c = m ln p which for m = 1.965 yields T c = 0.8943 and for m = p 1/3 yields T c = 0.9467. In figure 5 we have presented our results for the energy and the Polyakov loop.…”

Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N

“…This is a weakly coupled moduli regime we will discuss in section 2.2. However D0-branes can compose a bound state too and the quantities scale as ∼ N 2 T and Φ ∼ (λ0T ) 1/4 for small λ eff [41,45]. Indeed the scaling for the scalar differs from the naive dimensional analysis (2.4) due to the large fluctuations of the thermal zero modes.…”

“…We also consider compactifying the theory on a spatial circle, which allows for phase transitions with dual Gregory-Laflamme descriptions [38][39][40][41][42]. Using the ideas of [35], we argue that the moduli theory encodes all the strongly coupled phases, and also predicts where transitions will occur.…”

“…We have omitted this phase transition in figure 1, since it is beyond the scope of this paper. See [41,42] for the analytic calculation of this transition.…”