Deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3 from supersymmetric matrix quantum mechanics

TL;DR

This paper demonstrates that supersymmetric matrix quantum mechanics with mass deformation can effectively model the deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3, aligning with predictions from gauge-gravity duality.

Contribution

It provides a new analytical and numerical approach to study phase transitions in N=4 super Yang-Mills theory using supersymmetric matrix quantum mechanics with mass deformation.

Findings

Reproduces the deconfinement phase transition at weak coupling

Shows the method can be extended to other space-time geometries

Validates the approach through analytical and numerical results

Abstract

We test the recent claim that supersymmetric matrix quantum mechanics with mass deformation preserving maximal supersymmetry can be used to study N=4 super Yang-Mills theory on RxS^3 in the planar limit. When the mass parameter is large, we can integrate out all the massive fluctuations around a particular classical solution, which corresponds to RxS^3. The resulting effective theory for the gauge field moduli at finite temperature is studied both analytically and numerically, and shown to reproduce the deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3 at weak coupling. This transition was speculated to be a continuation of the conjectured phase transition at strong coupling, which corresponds to the Hawking-Page transition based on the gauge-gravity duality. By choosing a different classical solution of the same model, one can also reproduce results for gauge theories on other space-time such as RxS^3/Z_q and RxS^2. All these theories can be studied at strong coupling by the new simulation method, which was used successfully for supersymmetric matrix quantum mechanics without mass deformation.