Instantons, supersymmetric vacua, and emergent geometries

Details Instantons, supersymmetric vacua, and emergent geometries Instantons, supersymmetric vacua, and emergent geometries

2006-09-26

arxiv.org/abs/hep-th/0609186v3

Phys.Rev.D74:125013,2006

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 3 figures, latex. v2: references added, comments added. v3: accepted version in PRD

Scientific paper

10.1103/PhysRevD.74.125013

We study instanton solutions and superpotentials for the large number of vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills theory on $R\times S^2$ with sixteen supercharges. We get the superpotential in the weak coupling limit from the gauge theory description. We study the gravity description of these instantons. Perturbatively with respect to a background, they are Euclidean branes wrapping cycles in the dual gravity background. Moreover, the superpotential can be given by the energy of the electric charge system characterizing each vacuum. These charges are interpreted as the eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge theories. We also discuss qualitatively the emergence of the extra spatial dimensions appeared on the gravity side.

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