Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-06-16
J.Phys.A39:8675-8680,2006
Physics
High Energy Physics
High Energy Physics - Theory
6 pages. To be published in Jour. Phys. A
Scientific paper
10.1088/0305-4470/39/27/008
We consider the problem of a self-interacting scalar field nonminimally coupled to the three-dimensional BTZ metric such that its energy-momentum tensor evaluated on the BTZ metric vanishes. We prove that this system is equivalent to a self-dual system composed by a set of two first-order equations. The self-dual point is achieved by fixing one of the coupling constant of the potential in terms of the nonminimal coupling parameter. At the self-dual point and up to some boundary terms, the matter action evaluated on the BTZ metric is bounded below and above. These two bounds are saturated simultaneously yielding to a vanishing action for configurations satisfying the set of self-dual first-order equations.
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