Some No-go Theorems for String Duals of Non-relativistic Lifshitz-like Theories

Tadashi Takayanagi; Tatsuma Nishioka; Wei Li

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Some No-go Theorems for String Duals of Non-relativistic Lifshitz-like Theories

Wei Li, Tatsuma Nishioka, Tadashi Takayanagi

High Energy Physics - Theory · Submitted 4 Aug 2009

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The authors' main claim Under reasonable ansaetze, we prove that such gravity duals in the supergravities are not possible.

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arXiv ID0908.0363 (version 3)

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CitationTadashi Takayanagi, Tatsuma Nishioka, Wei Li. "Some No-go Theorems for String Duals of Non-relativistic Lifshitz-like Theories." arXiv:0908.0363 (2009). https://pith.science/paper/KJVRJFSV

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We study possibilities of string theory embeddings of the gravity duals for non-relativistic Lifshitz-like theories with anisotropic scale invariance. We search classical solutions in type IIA and eleven-dimensional supergravities which are expected to be dual to (2+1)-dimensional Lifshitz-like theories. Under reasonable ansaetze, we prove that such gravity duals in the supergravities are not possible. We also discuss a possible physical reason behind this.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study possibilities of string theory embeddings of the gravity duals for non-relativistic Lifshitz-like theories with anisotropic scale invariance.	contribution 0.86	0.86	0.04	asserted 0.52
s1	We search classical solutions in type IIA and eleven-dimensional supergravities which are expected to be dual to (2+1)-dimensional Lifshitz-like theories.	method 0.70	0.86	0.03	asserted 0.54
s2	Under reasonable ansaetze, we prove that such gravity duals in the supergravities are not possible.	result 1.00	0.95	0.95	asserted 1.00
s3	We also discuss a possible physical reason behind this.	interpretation 0.96	0.79	0.03	hedged possibility 0.75

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Original abstract

We study possibilities of string theory embeddings of the gravity duals for non-relativistic Lifshitz-like theories with anisotropic scale invariance. We search classical solutions in type IIA and eleven-dimensional supergravities which are expected to be dual to (2+1)-dimensional Lifshitz-like theories. Under reasonable ansaetze, we prove that such gravity duals in the supergravities are not possible. We also discuss a possible physical reason behind this.

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Cited by 15 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Towards strange metallic holography
hep-th 2009-12 accept novelty 7.0 of 10

Probe D-branes in a Lifshitz background give resistivity proportional to T^(2/z) divided by charge density, so a dynamical exponent z=2 reproduces the linear resistivity of strange metals.
Constructing Lifshitz solutions from AdS
hep-th 2011-02 accept novelty 6.0 of 10

Circle reduction with axion flux turns any AdS vacuum of a (d+1)-dimensional gravity theory into a z=2 Lifshitz solution in d dimensions, and N=2 AdS5 vacua yield 1/4-BPS Lifshitz4 backgrounds.
Lifshitz solutions in supergravity and string theory
hep-th 2010-09 conditional novelty 6.0 of 10

Explicit Li4 x H2 and Li3 x H2 Lifshitz solutions with general z >= 1 are found in Romans gauged supergravities and uplifted to massive Type IIA and Type IIB.
Lifshitz Solutions of D=10 and D=11 supergravity
hep-th 2010-08 accept novelty 6.0 of 10

Infinite families of exact z = 2 Lifshitz solutions of type IIB, type IIA and D = 11 supergravity are constructed from five- and seven-dimensional Einstein spaces, and are supersymmetric when those spaces are Sasaki-Einstein.
Lifshitz spacetimes from AdS null and cosmological solutions
hep-th 2010-05 conditional novelty 6.0 of 10

Null deformations of AdS5 x S5 with a scalar depending on a compact lightlike coordinate reduce, after Kaluza-Klein compactification, to four-dimensional z=2 Lifshitz spacetimes.

Show 10 more citing papers

Analytic Lifshitz black holes in higher dimensions
hep-th 2010-01 conditional novelty 6.0 of 10

New exact Lifshitz black hole solutions are found for higher-curvature gravity in arbitrary dimension and dynamical exponent, including an extremal case and a logarithmic-decay case.
An analytic Lifshitz black hole
hep-th 2009-09 conditional novelty 6.0 of 10

An exact black hole asymptoting to a z=2 Lifshitz geometry is constructed, its thermodynamics verified, and its scalar response computed in closed form, showing the dual correlators are not ultralocal.
Zero Temperature Limit of Holographic Superconductors
hep-th 2009-08 accept novelty 6.0 of 10

Holographic superconductors have no hard gap: the low-frequency conductivity remains nonzero at zero temperature because the effective Schrödinger potential always vanishes at the horizon.
Ground states of holographic superconductors
hep-th 2009-08 conditional novelty 6.0 of 10

For the Abelian Higgs model in AdS4, the infrared ground state is conformal when the scalar charge is large and Lifshitz-like when it is small, with Lifshitz the only constant-scalar alternative to AdS and Reissner-Nordstrom.
On the IR completion of geometries with hyperscaling violation
hep-th 2012-08 conditional novelty 5.0 of 10

Adding polynomial corrections to the gauge kinetic function stabilizes the dilaton at the horizon, producing an AdS2 x R2 infrared fixed point and a numerical flow from AdS4 through a hyperscaling violating region dow...
On Lifshitz scaling and hyperscaling violation in string theory
hep-th 2012-02 conditional novelty 5.0 of 10

Dimensional reduction of null-deformed AdS shock waves from D3, M2 and M5 brane near-horizon geometries yields effective gravity backgrounds with Lifshitz exponent z and hyperscaling violation theta, including (d=2, z...
Universal de Sitter solutions at tree-level
hep-th 2010-03 accept novelty 5.0 of 10

A class of classical de Sitter solutions in type IIA string theory can be written entirely in terms of universal SU(3)-structure data, and the known SU(2)xSU(2) solution is shown to be one of them.
Lifshitz Black Hole in Three Dimensions
hep-th 2009-09 conditional novelty 5.0 of 10

New Massive Gravity in three dimensions admits Lifshitz vacua for generic dynamical exponent z, and at z=3 an exact asymptotically Lifshitz black hole with a closed-form metric.
On Charged Lifshitz Black Holes
hep-th 2009-11 conditional novelty 4.0 of 10

Charged Lifshitz black holes exist in any dimension with dynamical exponent z = 2d, but their mass can only be fixed by the first law of thermodynamics because Hamiltonian and holographic mass prescriptions diverge.
Lifshitz holography
hep-th 2015-12 conditional novelty 3.0 of 10

A structured review of the holographic dictionary for Lifshitz backgrounds, arguing that the bulk matter supporting the geometry sources the non-relativistic energy-momentum complex plus scalar operators rather than a...

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33 arXiv papers cite this in 38 sentences

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Indeed, not only the known susy AdS solutions are universal, recently also classes of non-susy AdS solutions were found using a universal ansatz [ref] [This was furthermore used for constructing Lifshitz solutions in type II supergravity [ref] .

Universal de Sitter solutions at tree-level · Introduction · 0.96

Cites it as background 20 papers

While initially some no-go theorems seemed to exclude the possibility of embedding Lifshitz solutions in the full supergravity theory[ See for example [ref] .], explicit examples of 10-dimensional solutions with a Lifshitz factor were constructed in [ref] and subsequently generalised in [ref] , and, in the context of $𝒩=2$ gauged supergravity, in [ref] .

A Note on Supersymmetric Type II Solutions of Lifshitz Type · Introduction · 0.86
Previous attempts at string or supergravity constructions of such spacetimes $Lif_4$ include [ref] .

Lifshitz-like systems and AdS null deformations · Introduction · 0.97
Recently, the Lifshitz-type black holes [ref] have received considerable attentions since these may provide a model of generalizing AdS/CFT correspondence to non-relativistic condensed matter physics as the AdS/CMT correspondence [ref] .

Phase transitions for the Lifshitz black holes · Introduction · 0.97

What it cites · 31 sentences without a confident label

Compares with 3 papers

Then the requirement $dH=0$ argues that $H∝θ^xθ^yθ^r$ as is indeed so in our setups.[ Notice that the solution [ref] has vanishing $H$-flux.

On String Theory Duals of Lifshitz-like Fixed Points · Why String Duals of Lifshitz-like Points are Hard · 0.90
As opposed to the proofs of no-go theorems for de-Sitter spaces [ref] and flux backgrounds [ref] in supergravity, we need more detailed arguments due to the lack of the Lorentz symmetry.

Supergravity description of field theories on curved manifolds and a no go theorem · Introduction · 0.87
As opposed to the proofs of no-go theorems for de-Sitter spaces [ref] and flux backgrounds [ref] in supergravity, we need more detailed arguments due to the lack of the Lorentz symmetry.

Hierarchies from Fluxes in String Compactifications · Introduction · 0.87

Cites as background 29 papers

Let us first review the gravity dual $Li_4$ of Lifshitz-like fixed points in $2+1$ dimension, which was first presented in [ref] .

Gravity Duals of Lifshitz-like Fixed Points · Review of Gravity Duals of Lifshitz-like Fixed Points · 0.99
Recently, two interesting extensions of the AdS/CFT correspondence [ref] to non-relativistic systems were proposed in the papers [ref] and [ref] .

The Large N Limit of Superconformal Field Theories and Supergravity · Introduction · 0.91
Recently, two interesting extensions of the AdS/CFT correspondence [ref] to non-relativistic systems were proposed in the papers [ref] and [ref] .

Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry · Introduction · 0.91

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