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Conductivity in the gravity dual to massive ABJM and the membrane paradigm
High Energy Physics - Theory · Submitted 5 Jun 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find the same result, showing an increase in conductivity, using two types of membrane paradigm computations.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we analyze the effect of the massive deformation of the ABJM model on the calculation of conductivity of the dual theory. | contribution 0.90 | 0.82 | 0.07 | asserted 0.52 |
| s1 | 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${}_{4}$. | method 0.69 | 0.86 | 0.30 | asserted 0.81 |
| s2 | 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. | method 1.00 | 0.90 | 0.05 | asserted 0.99 |
| s3 | We find the same result, showing an increase in conductivity, using two types of membrane paradigm computations. | result 1.00 | 0.96 | 0.59 | asserted 1.00 |
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The paper
Original 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.
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How the literature uses it
3 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Uses its method or tool 1 paper
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The AdS/CFT calculations using the membrane paradigm will be based on the original work of Iqbal and Liu [ref] (see also [ref] ), as well as Kovtun, Son and Starinets [ref] We we also treat quantum corrections to the gravitational action and the Maxwell and scalar fields in it, following the formalism of [ref] .
Particle-vortex duality and theta terms in AdS/CMT applications · Introduction · 0.99
What it cites · 21 sentences without a confident label
Builds on 1 paper
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We want to generalize the calculation of [ref] to include the effect of the mass deformation, however we will find that we can only calculate the DC conductivity, $σ(0)$.
Holographic Quantum Critical Transport without Self-Duality · Introduction · 1.00
Uses the method or tool of 3 papers
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Following [ref] , we need to add a boundary term at the horizon to the one that arises from variations of this action.
An Action for Black Hole Membranes · Scalar field calculation · 0.91
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One way to relate to the conductivity at the boundary is to study the $r$ dependence of the current $j^i$ and electric field $F_ti$, by looking at the equation of motion and Bianchi identities involving $_r j^i$ and $_r F_ti$ along the lines of Appendix B in [ref] .
Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm · Conductivity using $J^i$ vs. $F_ti$ relation in the presence of $g_rt$ · 0.99
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The general ansatz for the truncation of the metric on an $n$-sphere $S^n$ down to $d$ dimensions is [ref] (here $D=d+n$) ds_D^2=Δ^-2/d-2ds_d^2+Δ^Ṯ_AB^-1DY^ADY^B where = 2/n-1d-1/d-2, Δ^2-ṉ = T^ABY_AY_B, DY^A = dY^A+B^ABY^B.Here $Y^A(y)$, with $A=0,...,n$, the scalar spherical harmonics on the sphere parametrized by $y⃗$ intrinsic coordinates, are also coordinates for the Euclidean embedding of the sphere, i.e. $Y^AY^A=1$.
On the nonlinear KK reductions on spheres of supergravity theories · First order deformation near the horizon · 0.93
Compares with 2 papers
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We can readily check that both of the formulas above give the correct result when the mass deformation is absent, namely [ref] σ_mb^A →1/g_4^2(1+4γ).
Holographic Quantum Critical Transport without Self-Duality · Conductivity using $J^i$ vs. $F_ti$ relation in the presence of $g_rt$ · 0.81
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This also matches with another expression found in [ref] , for $T_AB=X_Aδ_AB$, with ds_D^2=(X_AY_A^2)^2/d-1ds_d^2+(X_AY_A^2)^-d-3/d-1(X_A^-1dY_A^2).
Symmetric Potentials of Gauged Supergravities in Diverse Dimensions and Coulomb Branch of Gauge Theories · First order deformation near the horizon · 0.87
Cites as background 5 papers
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While the duality between type IIB superstrings on $AdS_5×S^5$ and $𝒩=4$ supersymmetric $SU(N)$ Yang-Mills theory remains the canonical example for such strong coupling computations, the recently discovered duality between type IIA superstrings on $AdS_4×ℂℙ^3$ and the so-called ABJM model [ref] , a $(2+1)-$dimensional $𝒩=6$, $U(N)×U(N)$ Chern-Simons-matter theory is quickly gaining ground in popularity.
N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Introduction · 0.98
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As alluded to in the introduction to this article, the ABJM model admits a mass deformation that, while obviously breaking its conformal symmetry, preserves its full $𝒩=6$ supersymmetry [ref] .
On M5-branes in N=6 Membrane Action · Massive deformation for ABJM black hole · 0.89
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As alluded to in the introduction to this article, the ABJM model admits a mass deformation that, while obviously breaking its conformal symmetry, preserves its full $𝒩=6$ supersymmetry [ref] .
A Massive Study of M2-brane Proposals · Massive deformation for ABJM black hole · 0.89
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