Approximate strange metallic behavior in AdS

Shesansu Sekhar Pal

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Approximate strange metallic behavior in AdS

Shesansu Sekhar Pal

High Energy Physics - Theory · Submitted 16 Feb 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show for unit dynamical exponent, $z=1$, the appearance of the Fermi liquid and non-Fermi liquid behavior as we tune the charge density and the magnetic field in 3+1 dimensional field theory using the gauge-gravity duality.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.82 · compares with prior results 0.08 · mentions code or data availability 0.02.

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We show for unit dynamical exponent, $z=1$, the appearance of the Fermi liquid and non-Fermi liquid behavior as we tune the charge density and the magnetic field in 3+1 dimensional field theory using the gauge-gravity duality. There exists an upturn behavior of the resistivity only along the direction perpendicular to the magnetic field. Also, there exists a universal behavior of the resistivity, independent of the dimensionality of the spacetime, in a specific corner of the parameter space, namely, in the large charge density and small magnetic field limit: the longitudinal conductivity goes as $T^{-2/z}$, whereas the Hall conductivity goes as $T^{-4/z}$. It means the Hall coefficient goes as $T^{4/z}$. We compute the diffusion constant from the flow equation of the conductivity.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show for unit dynamical exponent, $z=1$, the appearance of the Fermi liquid and non-Fermi liquid behavior as we tune the charge density and the magnetic field in 3+1 dimensional field theory using the gauge-gravity duality.	contribution 0.73	0.94	0.64	asserted 1.00
s1	There exists an upturn behavior of the resistivity only along the direction perpendicular to the magnetic field.	result 1.00	0.84	0.12	asserted 1.00
s2	Also, there exists a universal behavior of the resistivity, independent of the dimensionality of the spacetime, in a specific corner of the parameter space, namely, in the large charge density and small magnetic field limit: the longitudinal conductivity goes as $T^{-2/z}$, whereas the Hall conductivity goes as $T^{-4/z}$.	result 1.00	0.86	0.39	asserted 1.00
s3	It means the Hall coefficient goes as $T^{4/z}$.	interpretation 0.92	0.79	0.12	asserted 1.00
s4	We compute the diffusion constant from the flow equation of the conductivity.	method 0.81	0.94	0.05	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.81.

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The paper

Original abstract

We show for unit dynamical exponent, $z=1$, the appearance of the Fermi liquid and non-Fermi liquid behavior as we tune the charge density and the magnetic field in 3+1 dimensional field theory using the gauge-gravity duality. There exists an upturn behavior of the resistivity only along the direction perpendicular to the magnetic field. Also, there exists a universal behavior of the resistivity, independent of the dimensionality of the spacetime, in a specific corner of the parameter space, namely, in the large charge density and small magnetic field limit: the longitudinal conductivity goes as $T^{-2/z}$, whereas the Hall conductivity goes as $T^{-4/z}$. It means the Hall coefficient goes as $T^{4/z}$. We compute the diffusion constant from the flow equation of the conductivity.

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6 arXiv papers cite this in 7 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Uses its method or tool 1 paper

To do the computations, we shall use the flow equation technique of [ref] , which is done in [ref] and [ref] for the DBI system.

Fermi-like Liquid From Einstein-DBI-Dilaton System · Application: DC conductivity · 1.00

Compares with it 1 paper

Such a crossover was found in a $3+1$ dimensional field theory using a magnetic field in [ref] .

Fermi-like Liquid From Einstein-DBI-Dilaton System · Application: DC conductivity · 0.91

Cites it as background 3 papers

More recently, progress has been made in addressing different scalings between Hall angle and resistivity by holography [ref] .

DC and Hall conductivity in holographic massive Einstein-Maxwell-Dilaton gravity · Introduction · 0.80
It is already well known that the strongly coupled theory described by the probe branes has zero sound and diffusion modes [ref] .

A strongly coupled anyon material · The spectral function and poles · 0.97
Other works addressing on the linear-T resistivity and Hall angle can be found in [ref] for an incomplete list.

Linear and quadratic in temperature resistivity from holography · Introduction · 0.91

What it cites · 25 sentences without a confident label

Uses the method or tool of 12 papers

Using the explicit background geometry eq([ref]) and gauge field eq([ref]), results in the fluctuating current[The general form of the equations of motion and the current associated to the fluctuating fields are written down in [ref] .] at a constant slice of $r$ as J^(1)x = -T_b√(∏^d-3_i=1 g_w^iw^j)(g_ttg_yy_r A^(1)_x-iωB _rA^(0)_t A^(1)_y√(g_tt(g_rr+g_zzz'^2)-(_r A^(0)_t)^2)√(g_xxg_yy+B^2))J^(1)y = -T_b√(∏^d-3_i=1 g_w^iw^j)(g_ttg_xx_r A^(1)_y+iB_rA^(0)_t E^(1)√(g_tt(g_rr+g_zzz'^2)-(_r A^(0)_t)^2)√(g_xxg_yy+B^2))J^(1)i = -T_b√(∏^d-3_i=1 g_w^iw^j) (g_tt√(g_xx g_yy+B^2) g^ij_r A^(1)_j√( g_tt(g_rr+g_zzz'^2)-(_r A^(0)_t)^2)), where we have done the Fourier transformation of the (fluctuating) field with the convention of $e^i(kx-wt)$ and $E^(1)≡ωA^(1)_x+kA^(1)_t$.

RG flow of transport quantities · Case I: $g_ab(r, z)$ · 0.93
Now, we can use the arguments of the reality of the Legendre transformed action as in [ref] to find the constraints at $r_⋆$ as g_tt(r_⋆)g_xx(r_⋆)=E^2c^2_H = [g_ttg_xx(g_yyg_zz+B^2)+c^2_A_tg_ttg^2_xx]_r_⋆=E[c^2_A_t+g_xx(g_yyg_zz+B^2)g^2_xx]_r_⋆, where in the second equality of the second line, we have used the first equation.

Metallic AdS/CFT · Strange metallic behavior with $z=1$ · 0.98
The diffusion constant can be derived from the flow equation of the conductivity in the hydrodynamic limit [ref] .

Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm · Electric charge diffusion · 0.93

Compares with 5 papers

With $z=2$, we do get the desired result of the resistivity but not the Hall angle [ref] for NFL phase.

Towards strange metallic holography · Conclusion · 0.98
In passing, let us point out that in the zero charge density, vanishing magnetic field and trivial embedding function limit, the analysis for the DBI action reduces to that of the Maxwell system in [ref] .

Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm · Diffusion for zero charge density and with non-trivial embedding · 0.92
This form of the dc conductivity precisely matches with that written in [ref] , up to a redefinition of the axion and with [ref] up to a redefinition of the charge density.

AC Transport at Holographic Quantum Hall Transitions · Flow equation with DBI and Chern-Simon term · 1.00

Cites as support 2 papers

There exists another motivation to consider the asymptotically AdS spacetime: in a recent study using the bottom up approach, it is shown that the Lifshitz spacetimes are unstable [ref] and [ref] .

Pathologies in Asymptotically Lifshitz Spacetimes · Introduction · 1.00
There exists another motivation to consider the asymptotically AdS spacetime: in a recent study using the bottom up approach, it is shown that the Lifshitz spacetimes are unstable [ref] and [ref] .

Lifshitz Singularities · Introduction · 1.00

Cites as background 5 papers

The spacetime that shows this particular value of the dynamical exponent are called as Lifshitz spacetime in [ref] .

Gravity Duals of Lifshitz-like Fixed Points · Strange metallic behavior with $z=1$ · 0.97
We mention, in passing, that there exists yet another approach to understand the NFL state, [ref] , [ref] , [ref] , [ref] , which is completely different from the previous approaches in a very important way: the basic degrees of freedom considered to be fermionic in nature.

Emergent quantum criticality, Fermi surfaces, and AdS2 · The approach · 0.98
We mention, in passing, that there exists yet another approach to understand the NFL state, [ref] , [ref] , [ref] , [ref] , which is completely different from the previous approaches in a very important way: the basic degrees of freedom considered to be fermionic in nature.

Semi-Holographic Fermi Liquids · The approach · 0.98

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