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From AdS to Schr\"odinger/Lifshitz dual space-times without or with hyperscaling violation
High Energy Physics - Theory · Submitted 5 Jun 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is observed that the (intersecting) branes of M/string theory, which are known to give AdS geometry (directly or upto a conformal transformation) in the near horizon limit, do also lead to Schr\" odinger/Lifshitz dual space-times (without or with hyperscaling violation) upon using appropriate solution generating transformation and dimensional reduction.
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It is observed that the (intersecting) branes of M/string theory, which are known to give AdS geometry (directly or upto a conformal transformation) in the near horizon limit, do also lead to Schr\" odinger/Lifshitz dual space-times (without or with hyperscaling violation) upon using appropriate solution generating transformation and dimensional reduction. We show that the dynamical exponents of the Schr\" odinger and the Lifshitz space-times obtained in this way always add upto 2. We illustrate this by several examples, including M2-, M5-branes of M-theory and D$(p+1)$-branes ($p\neq 4$, since in this case the near horizon limit does not give AdS geometry) of string theory as well as many of their intersecting solutions. The Schr\" odinger space-time can be obtained by the standard wave generating technique along one of the brane directions (for single brane) or one of the common brane directions (for intersecting branes) and then interchanging the light-cone coordinates by double Wick rotations, whereas, the Lifshitz space-time can be obtained by dimensionally reducing (for M-theory) along the wave direction or taking T-duality (for string theory) along the same direction. We thus obtain Schr\" odinger/Lifshitz dual space-times without or with hyperscaling violation from the same M/string theory solutions and they preserve some fraction of the supersymmetry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It is observed that the (intersecting) branes of M/string theory, which are known to give AdS geometry (directly or upto a conformal transformation) in the near horizon limit, do also lead to Schr\" odinger/Lifshitz dual space-times (without or with hyperscaling violation) upon using appropriate solution generating transformation and dimensional reduction. | result 0.76 | 0.46 | 0.67 | asserted 0.99 |
| s1 | We show that the dynamical exponents of the Schr\" odinger and the Lifshitz space-times obtained in this way always add upto 2. | result 1.00 | 0.92 | 0.62 | asserted 1.00 |
| s2 | We illustrate this by several examples, including M2-, M5-branes of M-theory and D$(p+1)$-branes ($p\neq 4$, since in this case the near horizon limit does not give AdS geometry) of string theory as well as many of their intersecting solutions. | contribution 0.86 | 0.80 | 0.08 | asserted 0.98 |
| s3 | The Schr\" odinger space-time can be obtained by the standard wave generating technique along one of the brane directions (for single brane) or one of the common brane directions (for intersecting branes) and then interchanging the light-cone coordinates by double Wick rotations, whereas, the Lifshitz space-time can be obtained by dimensionally reducing (for M-theory) along the wave direction or taking T-duality (for string theory) along the same direction. | method 1.00 | 0.68 | 0.07 | asserted 1.00 |
| s4 | We thus obtain Schr\" odinger/Lifshitz dual space-times without or with hyperscaling violation from the same M/string theory solutions and they preserve some fraction of the supersymmetry. | result 0.84 | 0.93 | 0.45 | asserted 1.00 |
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Original abstract
It is observed that the (intersecting) branes of M/string theory, which are known to give AdS geometry (directly or upto a conformal transformation) in the near horizon limit, do also lead to Schr\" odinger/Lifshitz dual space-times (without or with hyperscaling violation) upon using appropriate solution generating transformation and dimensional reduction. We show that the dynamical exponents of the Schr\" odinger and the Lifshitz space-times obtained in this way always add upto 2. We illustrate this by several examples, including M2-, M5-branes of M-theory and D$(p+1)$-branes ($p\neq 4$, since in this case the near horizon limit does not give AdS geometry) of string theory as well as many of their intersecting solutions. The Schr\" odinger space-time can be obtained by the standard wave generating technique along one of the brane directions (for single brane) or one of the common brane directions (for intersecting branes) and then interchanging the light-cone coordinates by double Wick rotations, whereas, the Lifshitz space-time can be obtained by dimensionally reducing (for M-theory) along the wave direction or taking T-duality (for string theory) along the same direction. We thus obtain Schr\" odinger/Lifshitz dual space-times without or with hyperscaling violation from the same M/string theory solutions and they preserve some fraction of the supersymmetry.
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How the literature uses it
3 arXiv papers cite this in 3 sentences
Papers citing it · 1 sentence without a confident label
Cites it as background 2 papers
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They have since been realized as solutions in “top-down” models obtained from string theory: the case $z=2$ proves to be the simplest to realize [ref] , but a construction allowing for general values of $z$ was given in [ref] .
Lifshitz flows in IIB and dual field theories · Introduction · 0.89
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Additionally, there are a set of “hyperscaling-violating” solutions which still have a Lifshitz-like symmetry, proposed in [ref] and studied further in [ref] .
What do non-relativistic CFTs tell us about Lifshitz spacetimes? · Introduction · 0.97
What it cites · 36 sentences without a confident label
Uses data or values from 1 paper
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This solution has, as discussed in [ref] , dynamical critical exponent $z=5/2$, the spatial dimension of boundary theory $d=1$ and the hyperscaling violation exponent $θ=1/2$.
Lifshitz-like space-time from intersecting branes in string/M theory · M2-brane · 0.95
Compares with 5 papers
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In fact we recognize this solution as the near horizon limit of the 1/4 BPS, F-D$p$ solution found in [ref] .
Lifshitz-like space-time from intersecting branes in string/M theory · D(p+1)-branes · 0.87
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Also it can be checked that their general formula of $z$ and $θ$ given in eqs.(6.43) and (6.44) for Lifshitz space-times in [ref] match with the results given in sections 3 and 4 of our paper for different values of the parameters defined in [ref] .
Holographic Models for Theories with Hyperscaling Violation · Conclusion · 1.00
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In fact we notice that the above solution is nothing but the near horizon limit of D0-D4 solution discussed in [ref] .
Intersecting D-branes and Lifshitz-like space-time · M5-brane · 0.95
Cites as background 11 papers
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Among them the ones which yield AdS$_3$ (AdS$_2$ is excluded as we mentioned) geometry are M2 $⊥$ M5 and M5 $⊥$ M5 $⊥$ M5 [ref] of M-theory and D1 $⊥$ D5, D2 $⊥$ D4, D3 $⊥$ D3 and F $⊥$ NS5 [ref] of type II string theories (the solutions involving triple intersections of string theory branes are not known explicitly and even if they give AdS geometry, they will either give AdS$_3$ or AdS$_2$ similar to the solutions involving double intersections and therefore we will not consider them here to avoid repetitions).
Lifshitz-like space-time from intersecting branes in string/M theory · Introduction · 0.81
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Among them the ones which yield AdS$_3$ (AdS$_2$ is excluded as we mentioned) geometry are M2 $⊥$ M5 and M5 $⊥$ M5 $⊥$ M5 [ref] of M-theory and D1 $⊥$ D5, D2 $⊥$ D4, D3 $⊥$ D3 and F $⊥$ NS5 [ref] of type II string theories (the solutions involving triple intersections of string theory branes are not known explicitly and even if they give AdS geometry, they will either give AdS$_3$ or AdS$_2$ similar to the solutions involving double intersections and therefore we will not consider them here to avoid repetitions).
Intersecting D-branes and Lifshitz-like space-time · Introduction · 0.81
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The gravity dual of Lifshitz metric was first obtained in [ref] .
Gravity Duals of Lifshitz-like Fixed Points · Introduction · 0.85
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