Analogies between self-duality and stealth matter source

Analogies between self-duality and stealth matter source
Canals Gustavo Adolfo (Talca U. & CECS, Valdivia,Ch.)
CECS-PHY-06-15, Jun 2008. 6pp.
Published in J.Phys.A39:8722-8680,2008.
e-Print: hep-th/0606763

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.

Canals Gustavo Adolfo
Dr.Física Teórica; Ph.D.math.
Talca U. & CECS, Valdivia,Ch.
adolfocanals@educ.ar