Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-11-30
JHEP 0103:008,2001
Physics
High Energy Physics
High Energy Physics - Theory
30 pages, 9 figures, Latex; interpretation of the supergravity solutions corrected, other results and ref. added
Scientific paper
10.1088/1126-6708/2001/03/008
We construct dual supergravity descriptions of D3-branes wrapping associative 3-cycles $L$. We analyse the conditions for having five-dimensional background solutions of the form $AdS_2 \times L$ and show that they require $L$ to be of constant negative curvature type. This provides $AdS_2$ background solutions when $L$ is the hyperbolic space $H^3$ or its quotients by subgroups of its isometry group. We construct a regular numerical solution interpolating between $AdS_5$ in the UV and $AdS_2 \times H^3$ in the IR. The IR fixed point exists at the ``intersection'' of the Coulomb and Higgs branches. We analyse the singular supergravity solutions which correspond to moving into the Higgs and the Coulomb branches. For negative constant curvature spaces the singularity is of a ``good'' type in the Higgs branch and of a ``bad'' type in the Coulomb branch. For positive constant curvature spaces such as $S^3$ the singularity is of a ``bad'' type in both the Higgs and the Coulomb branches. We discuss the meaning of these results.
Nieder Harald
Oz Yaron
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