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

Umut Gursoy·Sean A. Hartnoll·Timothy J. Hollowood·S. Prem Kumar
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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, Φ_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/(\sqrtλR_{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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Umut Gursoy, Sean A. Hartnoll, Timothy J. Hollowood, S. Prem Kumar. 2007-08-21. Topology change in commuting saddles of thermal N=4 SYM theory. https://doi.org/10.1088/1126-6708%2F2007%2F11%2F020

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