Emergent geometry of membranes

Badyn, Mathias Hudoba de; Karczmarek, Joanna L.; Sabella-Garnier, Philippe; Yeh, Ken Huai-Che

doi:10.48550/arxiv.1506.02035

Cited by 4 publications

(16 citation statements)

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“…In this context, the idea of emergent gravity has been pursued [10][11][12][13][14][15][16][17] in gauge theories on non-commutative space that appear from the type IIB matrix model for a particular class of backgrounds [18][19][20][21]. There are also other proposals for the description of curved space-time in matrix models [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model

Ito

Nishimura

Tsuchiya

2015

J. High Energ. Phys.

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Recent studies on the Lorentzian version of the type IIB matrix model show that (3+1)D expanding universe emerges dynamically from (9+1)D space-time predicted by superstring theory. Here we study a bosonic matrix model obtained by omitting the fermionic matrices. With the adopted simplification and the usage of a large-scale parallel computer, we are able to perform Monte Carlo calculations with matrix size up to N = 512, which is twenty times larger than that used previously for the studies of the original model. When the matrix size is larger than some critical value N c 110, we find that (3+1)D expanding universe emerges dynamically with a clear large-N scaling property. Furthermore, the observed increase of the spatial extent with time t at sufficiently late times is consistent with a power-law behavior t 1/2 , which is reminiscent of the expanding behavior of the Friedmann-Robertson-Walker universe in the radiation dominated era. We discuss possible implications of this result on the original supersymmetric model including fermionic matrices.

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Section: Introductionmentioning

confidence: 99%

Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model

Ito

Nishimura

Tsuchiya

2015

J. High Energ. Phys.

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“…In summary, the tachyon condensation just picks up the zeros of the eigenfunction and as a result a defect remains on a region M. This is technically the same as the coherent state method mentioned in the introduction. In fact, the tachyon profile T (2.1) is exactly the same as the Dirac-like operator in the literature [12,13,14,17] and T 2 corresponds to the Hamiltonian in [15,16]. Our claim in this paper is that the tachyon condensation gives a new physical interpretation of this prescription, based on the dynamics of the non-BPS D-branes.…”

Section: Tachyon Condensation and Gauge Flux Productionmentioning

confidence: 66%

“…The energy of the open string can be measured by using a Dirac operator on the open strings and thus the shape of NC branes is defined as loci of zeros of the Dirac operator. See also [13,14] for analysis of this method.…”

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confidence: 99%

Commutative geometry for non-commutative D-branes by tachyon condensation

Asakawa

Ishiki

Matsumoto

et al. 2018

Progress of Theoretical and Experimental Physics

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There is a difficulty in defining the positions of the D-branes when the scalar fields on them are non-abelian. We show that we can use tachyon condensation to determine the position or the shape of D0-branes uniquely as a commutative region in spacetime together with non-trivial gauge flux on it, even if the scalar fields are non-abelian. We use the idea of the so-called coherent state method developed in the field of matrix models in the context of the tachyon condensation. We investigate configurations of noncommutative D2-brane made out of D0-branes as examples. In particular, we examine a Moyal plane and a fuzzy sphere in detail, and show that whose shapes are commutative R 2 and S 2 , respectively, equipped with uniform magnetic flux on them. We study the physical meaning of this commutative geometry made out of matrices, and propose an interpretation in terms of K-homology.

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“…In [7] it was shown that these two approaches can be based on the same footing. In [6] two-dimensional surfaces emerging from the Hamiltonian defined in [5] were studied in more detail. Interestingly, for the more symmetric fuzzy spaces, which mainly are based on coadjoint orbits of Lie groups, the set of coherent states are very similar to the coadjoint orbit (seen as a manifold).…”

Section: Introductionmentioning

confidence: 99%

“…In the following chapter 2, we mainly review the content of [4,5,6,7], which will be used in the following chapter 3. In general, the set of coherent states can be defined based on a Laplace operator [5] or a Dirac operator [4].…”

Section: Introductionmentioning

confidence: 99%

The fuzzy space construction kit

Sykora

2016

Preprint

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Fuzzy spaces like the fuzzy sphere or the fuzzy torus have received remarkable attention, since they appeared as objects in string theory. Although there are many higher dimensional examples, the most known and most studied fuzzy spaces are realized as matrix algebras defined by three Hermitian matrices, which may be seen as fuzzy membranes or fuzzy surfaces. We give a mapping between directed graphs and matrix algebras defined by three Hermitian matrices and show that the matrix algebras of known two-dimensional fuzzy spaces are associated with unbranched graphs. By including branchings into the graphs we find matrix algebras that represent fuzzy spaces associated with surfaces having genus 2 and higher.

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Emergent geometry of membranes

Cited by 4 publications

References 0 publications

Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model

Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model

Commutative geometry for non-commutative D-branes by tachyon condensation

The fuzzy space construction kit

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