Abstract
We obtain (2+1) dimensional p-wave holographic superconductors from charged Born-Infeld black holes in the presence of massive charged vector fields in a bulk AdS4 Einstein-Born-Infeld theory through the AdS4-CF T3 correspondence. Below a certain critical transition temperature the charged black hole develops vector hair that corresponds to charged vector condensate in the strongly coupled (2+1) dimensional boundary field theory that breaks both the U(1) symmetry as well as the rotational invariance. The holographic free energy is computed for the boundary field theory which shows that the vector order parameter exhibits a rich phase structure involving zeroth order, first order, second order and retrograde phase transitions for different values of the backreaction and the Born-Infeld parameters. We numerically compute the ac conductivity for the p-wave superconducting phase of the strongly coupled (2+1) dimensional boundary field theory which also depends on the relative values of the parameters in the theory.
Highlights
JHEP04(2015)001 model with a bulk complex scalar field that is charged under the Maxwell field [8,9,10,11,12]
Whereas in [28], it was observed that depending on the mass of the complex vector field and the strength of the backreaction, the condensate formation may occur through a first order, second order, zeroth order [29] or a retrograde phase transition [30]
It is possible to include a non-minimal coupling [28] between the vector field and the gauge field in the bulk Einstein Born-Infeld theory that represents the magnetic moment of the complex vector field and plays a crucial role for the condensate formation induced by an external magnetic field
Summary
In order to realize a vector condensate in the Einstein-Born-Infeld theory we consider a bulk gravitational action with a complex vector field [28] that is charged under the bulk Maxwell field associated with the Born-Infeld Lagrangian. The last term in the expression for the matter Lagrangian represents the non-minimal coupling between the vector field ρμ and the gauge field Aμ. In our study we will neglect the effect of the interaction term on the boundary field theory and consider only the effect of the nonlinear Born-Infeld term For this purpose we will set the interaction parameter η to zero at the level of the ansatz for solving the equations of motion. In our model we consider the backreaction of the bulk fields on the background metric that describes a charged Born-Infeld black hole in the AdS4 bulk. We find the equations of the motion for the bulk matter fields through the variation of the action (2.1) as
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