Exact Abelian Higgs vortices as 6d brane worlds
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04.20.-q, 11.27. d, 04.50. hAbstract
In this work we report new exact solutions to Nielsen Olesen vortex equations for the Abelian Higgs model in flat 3 dimensional and curved 6 dimensional space times. In the 3D flat case, choosing suitable boundary conditions we found a complete equivalence between the string vortex equations for the mexican hat potential and non linear schrödinger equations. We also present an exact vortex solution with a new potential similar in shape to the mexican hat. In 6D we found new string vortex solutions to the einstein equations for 3 different symmetry breaking potentials. Just as happens for RS domain wall brane worlds, we show that the massless mode of linearized gravity is localized in the neighborhood of the vortex solution. We also show that there are not massive bounded states and found the correction to the newtonian limit of the effective gravity.
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