Topology change in commuting saddles of thermal N=4 SYM theory

TL;DR

This paper investigates how the topology of eigenvalue distributions in thermal N=4 SYM theory changes from S^1 x S^5 to S^6 at high temperatures, revealing a continuous second order phase transition.

Contribution

It demonstrates the topology change in eigenvalue distributions at the deconfinement transition and identifies a new second order quantum phase transition at a specific temperature.

Findings

Eigenvalue distribution topology shifts from S^1 x S^5 to S^6 at high temperature.

Deconfinement transition corresponds to a topology change in the eigenvalue space.

Evidence of a second order quantum phase transition at T = 1/(\sqrt ext{λ} R_{S^3}).

Abstract

We study the large N saddle points of weakly coupled N=4 super Yang-Mills theory on S^1 x S^3 that are described by a commuting matrix model for the seven scalar fields {A_0, \Phi_J}. We show that at temperatures below the Hagedorn/`deconfinement' transition the joint eigenvalue distribution is S^1 x S^5. At high temperatures T >> 1/R_{S^3}, the eigenvalues form an ellipsoid with topology S^6. We show how the deconfinement transition realises the topology change S^1 x S^5 --> S^6. Furthermore, we find compelling evidence that when the temperature is increased to T = 1/(\sqrt\lambda R_{S^3}) the saddle with S^6 topology changes continuously to one with S^5 topology in a new second order quantum phase transition occurring in these saddles.