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

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

2007-03-09

arxiv.org/abs/hep-th/0703100v2

JHEP 0711:020,2007

Physics

High Energy Physics

High Energy Physics - Theory

1+40 pages, 6 figures. v2: Title changed. Status of commuting saddles clarified: New high T phase transition claimed in the co

Scientific paper

10.1088/1126-6708/2007/11/020

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.

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