Abstract
We explore the momentum analyticity of the static transverse polarization tensor of a 2+1 dimensional holographic superconductor in its normal phase with a nonzero chemical potential, aiming at finding the holographic counterpart of the singularities underlying the Friedel-like oscillations of an ordinary field theory. We prove that the polarization tensor is a meromorphic function with an infinite number of poles located on the complex momentum plane off real axis. With the aid of the WKB approximation these poles are found to lies asymptotically along two straight lines parallel to the imaginary axis for a large momentum magnitude. The similarity between the holographic Green's function and that of an weakly coupled ordinary field theory (e.g., 2+1 dimensional QED) regarding the location of the momentum singularities offers further support to the validity of the gauge/gravity duality.
Highlights
Holographic models, it is important to examine if the quantum effective action implied by holography possesses all fundamental properties of an ordinary field theory
We explore the momentum analyticity of the static transverse polarization tensor of a 2+1 dimensional holographic superconductor in its normal phase, aiming at finding the holographic counterpart of the singularities underlying the Friedel oscillations of an ordinary field theory
We prove that the polarization tensor is a meromorphic function with an infinite number of poles located on the complex momentum plane off real axis
Summary
The Gauge/Gravity correspondence employed in this work is encoded in the following relationship between a classical gravity-matter system in the bulk spacetime and a strongly coupled quantum field theory at the asymptotically AdS boundary. L is the AdS radius, and KD is the coupling constant in D = d + 1 dimensional spacetime This action at d = 3 corresponds to the normal phase of the 2-dimensional holographic superconductivity, where the scalar field vanishes, investigated extensively in literature. The presence of the 2-form field Fμν = ∂μAν − ∂νAμ leads to a solution of equations of motion which consists of a charged RN-AdS black hole, given by the metric and a background gauge potential. Where z+ is the coordinate of the horizon, Q is the charge of the black hole and μ corresponds to the chemical potential of the boundary field theory. The solution (3.3) and (3.5) define a thermal bath of the boundary field theory
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