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Modified Einstein equations from the 1-loop effective action of the IKKT model
High Energy Physics - Theory · Submitted 3 Dec 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resulting gravity theory approximately reduces to general relativity in some regime, but differs significantly at cosmic scales, leading to an asymptotically flat FLWR cosmological evolution governed by the classical action.
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The abstract, sentence by sentence
We derive the equations of motion that arise from the one-loop effective action for the geometry of 3+1 dimensional quantum branes in the IKKT matrix model. These equations are cast into the form of generalized Einstein equations, with extra contributions from dilaton and axionic fields, as well as a novel anharmonicity tensor C_{\mu\nu} capturing the classical Yang-Mills-type action. The resulting gravity theory approximately reduces to general relativity in some regime, but differs significantly at cosmic scales, leading to an asymptotically flat FLWR cosmological evolution governed by the classical action.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We derive the equations of motion that arise from the one-loop effective action for the geometry of 3+1 dimensional quantum branes in the IKKT matrix model. | contribution 0.96 | 0.96 | 0.13 | asserted 1.00 |
| s1 | These equations are cast into the form of generalized Einstein equations, with extra contributions from dilaton and axionic fields, as well as a novel anharmonicity tensor C_{\mu\nu} capturing the classical Yang-Mills-type action. | result 0.86 | 0.91 | 0.33 | asserted 1.00 |
| s2 | The resulting gravity theory approximately reduces to general relativity in some regime, but differs significantly at cosmic scales, leading to an asymptotically flat FLWR cosmological evolution governed by the classical action. | result 0.59 | 0.86 | 0.62 | asserted 0.88 |
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The paper
Original abstract
We derive the equations of motion that arise from the one-loop effective action for the geometry of 3+1 dimensional quantum branes in the IKKT matrix model. These equations are cast into the form of generalized Einstein equations, with extra contributions from dilaton and axionic fields, as well as a novel anharmonicity tensor C_{\mu\nu} capturing the classical Yang-Mills-type action. The resulting gravity theory approximately reduces to general relativity in some regime, but differs significantly at cosmic scales, leading to an asymptotically flat FLWR cosmological evolution governed by the classical action.
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References
How the literature uses it
4 arXiv papers cite this in 8 sentences
Papers citing it · 3 sentences without a confident label
Builds on it 1 paper
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We now elaborate further the one-loop effective action for the geometric or gravitational sector of on the present $^1,3_×$ background, as initiated in [ref] .
$\mathfrak{hs}$-extended gravity from the IKKT matrix model · Emergent hs-extended gravity at one loop · 0.94
Cites it as background 4 papers
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The resulting $$ gauge theory has several peculiar features, see e.g. [ref] for recent studies.
$\mathfrak{hs}$-extended gravity from the IKKT matrix model · Introduction · 0.92
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For some pertinent recent development in this direction see e.g. [ref] , and [ref] for numerical investigation of the emergence of space-time within this model.
Quantum $\mathfrak{hs}$-Yang-Mills from the IKKT matrix model · Introduction · 0.86
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Similar deformations led also to other classical backgrounds, where gravity can arise from the one-loop effective action at weak coupling [ref] .
The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations · Introduction · 0.86
What it cites · 24 sentences without a confident label
Uses the method or tool of 1 paper
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First of all, a straightforward computation involving [ref] yields [equation] Furthermore, the term involving $δT_ν$ simplifies as follows (see [ref] ): [equation] where in the last line we have employed the following definition of $T_ρ$ which is equivalent to [ref] [equation] The last part of this integral can be computed as follows: [equation] where we have used the definition of the torsion [ref] and [ref] in the second step and integration by parts in the third one.
Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution · Variation of $Γ_$ · 0.85
Cites as support 1 paper
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A more careful examination of the cosmological evolution at one loop [ref] suggests that the classical equations of motion indeed dominate over the induced one-loop effects, leading to a picture that is rather different from GR and less sensitive to the detailed matter content[At the classical level, matter does not act as a source for the curvature in the matrix model.].
One-loop effective action of the IKKT model for cosmological backgrounds · Emergent gravity from the one-loop effective action · 1.00
Cites as background 13 papers
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One specific proposal for such an underlying quantum theory is the IKKT matrix model, which is related to IIB string theory [ref] .
Space-Time Structures from IIB Matrix Model · Introduction · 0.97
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One specific proposal for such an underlying quantum theory is the IKKT matrix model, which is related to IIB string theory [ref] .
A Large-N Reduced Model as Superstring · Introduction · 0.97
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This approach is in the spirit of noncommutative gauge theory (cf. [ref] and references therein), where target space has no direct physical meaning, and is not inhabited by propagating fields; it therefore does not need to be compactified.
Noncommutative Field Theory · Introduction · 0.94
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