Topology change in commuting saddles of thermal N=4 SYM theory
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.
Keywords
Cite
@article{arxiv.hep-th/0703100,
title = {Topology change in commuting saddles of thermal N=4 SYM theory},
author = {Umut Gursoy and Sean A. Hartnoll and Timothy J. Hollowood and S. Prem Kumar},
journal= {arXiv preprint arXiv:hep-th/0703100},
year = {2011}
}
Comments
1+40 pages, 6 figures. v2: Title changed. Status of commuting saddles clarified: New high T phase transition claimed in the commuting sector only, not in the full theory