Conductivity in the gravity dual to massive ABJM and the membrane paradigm

TL;DR

This paper investigates how a massive deformation of the ABJM model affects the conductivity in its gravity dual, proposing a membrane paradigm approach to simplify calculations near black hole horizons.

Contribution

It introduces a membrane paradigm method to compute conductivity in deformed ABJM models, bypassing complex dual geometry constructions.

Findings

Deformation increases conductivity in the dual theory.

Membrane paradigm approach simplifies horizon calculations.

Consistent results obtained with two different methods.

Abstract

In this paper we analyze the effect of the massive deformation of the ABJM model on the calculation of conductivity of the dual theory. We show that some of the difficulties presented by the dual geometry, in particular the construction of black holes therein, can be at least partially circumvented by adopting a membrane paradigm-like computation of the conductivity, which requires us to know just the effect of the deformation on the {\it horizon} of a black hole in AdS${}_{4}$. The deformation at the horizon itself is found by first deforming the flat space near the horizon, and then using the corresponding solution near the horizon as initial conditions for the Einstein's equations. We find the same result, showing an increase in conductivity, using two types of membrane paradigm computations.