Gravity Dual of Gauge Theory on S^2 x S^1 x R

Details Gravity Dual of Gauge Theory on S^2 x S^1 x R Gravity Dual of Gauge Theory on S^2 x S^1 x R

2006-01-31

arxiv.org/abs/hep-th/0602003v2

JHEP0606:021,2006

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 4 figures, v2: minor changes, added references

Scientific paper

10.1088/1126-6708/2006/06/021

We (numerically) construct new static, asymptotically AdS solutions where the conformal infinity is the product of time and S^2 x S^1. There always exist a family of solutions in which the S^1 is not contractible and, for small S^1, there are two additional families of solutions in which the S^1 smoothly pinches off. This shows that (when fermions are antiperiodic around the S^1) there is a quantum phase transition in the gauge theory as one decreases the radius of the S^1 relative to the S^2. We also compare the masses of our solutions and argue that the one with lowest mass should minimize the energy among all solutions with conformal boundary S^2 x S^1 x R. This provides a new positive energy conjecture for asymptotically locally AdS metrics. A simple analytic continuation produces AdS black holes with topology S^2 x S^1.

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