Momentum analyticity of the holographic electric polarizability in 2 + 1 dimensions

Abstract

Abstract:The static electric polarization of a holographic field theory dual to the Einstein-Maxwell theory in the background of AdS 4 with a Reissner-Nordström (AdS-RN) black hole is investigated. We prove that the holographic polarization is a meromorphic functions in complex momentum plane and locate analytically the asymptotic distribution of the poles along two straight lines parallel to the imaginary axis for a large momentum magnitude. The results are compared with the numerical result on Friedel-like poles of the same holographic model reported in the literature and with the momentum singularities of the one-loop polarization in weak-coupling spinor QED 3 and scalar QED 3 with the similarities and differences discussed.

Holographic magnetic susceptibility

“…Their numerical solution also indicates an exponentially decaying Friedel-like oscillation behavior even at zero temperature. In our previous works [17] and [28], we were able to prove that both χ(0, q) and α(0, q) extracted from the non-extremal Reissner-Nordström-AdS geometry are meromorphic functions and to locate their poles analytically for large |Im q| via WKB solution of the Einstein-Maxwell equations. The asymptotic distribution of the poles is given by…”

“…The distinction between the real part of the branch cuts location in strong coupling and the location of the discontinuity 2µ in weak coupling is observed in other studies[27] and[33]. Throughout this paper, we follow the convention in our previous works[17] and[28] by scaling the U (1) gauge potential in eq (6). …”

“…For the full set of Einstein-Maxwell equations in terms of our notations, see [17,28]. The static magnetic susceptibility at a temperature T is given by…”

“…The analytic technique employed in this work is not yet to be generalized to the case of electrical polarization, α(0, q) in order to extend the result of Ref. [28] to zero temperature, in which case the Einstein-Maxwell equations involved are far more complicated. We hope to report our progress along this line in near future.…”

Study on a holographic static transverse polarization at non-zero temperature

“…(2) is represented as a ratio as shown in (12), therefore, in analytical work, for the small momentum expansion, we needn't to practically solve the equations ( 9) and (10). We put a short review on this analytical result in Appendix B.…”