Solving some gauge systems at infinite N

Details Solving some gauge systems at infinite N Solving some gauge systems at infinite N

2006-10-15

arxiv.org/abs/hep-th/0610172v2

ActaPhys.Polon.B37:3635-3658,2006

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 7 figures; lecture given at the XLVI Cracow School of Theoretical Physics; some typos and references corrected

Scientific paper

After summarizing briefly some numerical results for four-dimensional supersymmetric SU(2) Yang-Mills quantum mechanics, we review a recent study of systems with an infinite number of colours. We study in detail a particular supersymmetric matrix model which exhibits a phase transition, strong-weak duality, and a rich structure of supersymmetric vacua. In the planar and strong coupling limits, this field theoretical system is equivalent to a one-dimensional XXZ Heisenberg chain and, at the same time, to a gas of $q$-bosons. This not only reveals a hidden supersymmetry in these well-studied models; it also maps the intricate pattern of our supersymmetic vacua into that of the now-popular ground states of the XXZ chain.

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