Higher Order Terms in the Improved Mean Field Approximation for the IIB Matrix Model and the Emergence of Four-Dimensional Space-Time

We study the properties of the space-time that emerges dynamically from the matrix model for type IIB superstrings in ten dimensions. We calculate the free energy and the extent of space-time using the Gaussian expansion method up to the third order. Unlike previous works, we study the SO(d) symmetric vacua with all possible values of d within the range 2 ≤ d ≤ 7, and observe clear indication of plateaus in the parameter space of the Gaussian action, which is crucial for the results to be reliable. The obtained results indeed exhibit systematic dependence on d, which turns out to be surprisingly similar to what was observed recently in an analogous work on the six-dimensional version of the model. In particular, we find the following properties: i) the extent in the shrunken directions is given by a constant, which does not depend on d; ii) the ten-dimensional volume of the Euclidean space-time is given by a constant, which does not depend on d except for d = 2;iii) The free energy takes the minimum value at d = 3. Intuitive understanding of these results is given by using the low-energy effective theory and some Monte Carlo results.

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confidence: 99%

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confidence: 99%

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See 2 more Smart Citations

Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings

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Okubo

Sugino

2011

“…There have been lots of study on these models (see e.g. [22][23][24][25][26][27]), including very impressive numerical studies (e.g. [28]), but it is of course very plausible if we can develop an analytic approach to dissect such models.…”

Section: Jhep06(2015)062mentioning

confidence: 99%

Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models

Kawamoto

Kuroki

2015

In the previous study [1][2][3], we formulate a matrix model renormalization group based on the fuzzy spherical harmonics with which a notion of high/low energy can be attributed to matrix elements, and show that it exhibits locality and various similarity to the usual Wilsonian renormalization group of quantum field theory. In this work, we continue the renormalization group analysis of a matrix model with emphasis on nonlocal interactions where the fields on antipodal points are coupled. They are indeed generated in the renormalization group procedure and are tightly related to the noncommutative nature of the geometry. We aim at formulating renormalization group equations including such nonlocal interactions and finding existence of nontrivial field theory with antipodal interactions on the fuzzy sphere. We find several nontrivial fixed points and calculate the scaling dimensions associated with them. We also consider the noncommutative plane limit and then no consistent fixed point is found. This contrast between the fuzzy sphere limit and the noncommutative plane limit would be manifestation in our formalism of the claim given by Chu, Madore and Steinacker that the former does not have UV/IR mixing, while the latter does.

Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model

Anagnostopoulos

Azuma

Ito

et al. 2020

The IKKT matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In this model, spacetime is conjectured to emerge dynamically from the microscopic matrix degrees of freedom in the large-N limit. Indeed in the Lorentzian version, Monte Carlo studies suggested the emergence of (3+1)-dimensional expanding spacetime. Here we study the Euclidean version instead, and investigate an alternative scenario for dynamical compactification of extra dimensions via the spontaneous symmetry breaking (SSB) of 10D rotational symmetry. We perform numerical simulations based on the complex Langevin method (CLM) in order to avoid a severe sign problem. Furthermore, in order to avoid the singular-drift problem in the CLM, we deform the model and determine the SSB pattern as we vary the deformation parameter. From these results, we conclude that the original model has an SO(3) symmetric vacuum, which is consistent with previous results obtained by the Gaussian expansion method (GEM). We also apply the GEM to the deformed matrix model and find consistency with the results obtained by the CLM.