Results 1  10
of
70
Monte Carlo studies of the IIB matrix model at large N
, 2000
"... The lowenergy effective theory of the IIB matrix model developed by H. Aoki et al. is written down explicitly in terms of bosonic variables only. The effective theory is then studied by Monte Carlo simulations in order to investigate the possibility of a spontaneous breakdown of tendimensional Lor ..."
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Cited by 36 (6 self)
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The lowenergy effective theory of the IIB matrix model developed by H. Aoki et al. is written down explicitly in terms of bosonic variables only. The effective theory is then studied by Monte Carlo simulations in order to investigate the possibility of a spontaneous breakdown of tendimensional Lorentz invariance. The imaginary part of the effective action, which causes the socalled sign problem in the simulation, is dropped by hand. The extent of the eigenvalue distribution of the bosonic matrices shows a powerlaw largeN behavior, consistent with a simple branchedpolymer prediction. We observe, however, that the eigenvalue distribution becomes more and more isotropic in the tendimensional spacetime as we increase N . This suggests that if the spontaneous breakdown of Lorentz invariance really occurs in the IIB matrix model, a crucial rôle must be played by the imaginary part of the effective action.
Emergent Gravity and Noncommutative Branes from YangMills Matrix Models
, 2008
"... The framework of emergent gravity arising from YangMills matrix models is developed further, for general noncommutative branes embedded in R D. The effective metric on the brane turns out to have a universal form reminiscent of the open string metric, depending on the dynamical Poisson structure an ..."
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Cited by 32 (17 self)
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The framework of emergent gravity arising from YangMills matrix models is developed further, for general noncommutative branes embedded in R D. The effective metric on the brane turns out to have a universal form reminiscent of the open string metric, depending on the dynamical Poisson structure and the embedding metric in R D. A covariant form of the treelevel equations of motion is derived, and the Newtonian limit is discussed. This points to the necessity of branes in higher dimensions. The quantization is discussed qualitatively, which singles out the IKKT model as a prime candidate for a quantum theory of gravity coupled to matter. The Planck scale is then identified with the scale of N = 4 SUSY breaking. A mechanism for avoiding the cosmological constant
Convergent yangmills matrix theories
 JHEP
"... In this thesis, we discuss bosonic and supersymmetric YangMills matrix models with compact semisimple gauge group. We begin by finding convergence properties for the models. In the supersymmetric case, we show that the partition function converges when D = 4, 6 and 10, and that correlation functio ..."
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Cited by 20 (3 self)
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In this thesis, we discuss bosonic and supersymmetric YangMills matrix models with compact semisimple gauge group. We begin by finding convergence properties for the models. In the supersymmetric case, we show that the partition function converges when D = 4, 6 and 10, and that correlation functions of degree k < kc = 2(D − 3) are convergent independently of the group. In the bosonic case we show that the partition function is convergent when D ≥ Dc, and that correlation functions of degree k < kc are convergent, and calculate Dc and kc for each group. We move on to consider the supersymmetric theories in both their YangMills and cohomological formulations. Specialising to the case of SU(N) with large N, we find all quantities which are invariant under the supercharges. Finally we apply the deformation method of Moore, Nekrasov and Shatashvili directly to the supersymmetric YangMills model with D = 4. We find a deformation of the action which generates mass terms for all the matrix fields whilst preserving some supersymmetry. This allows us to rigorously integrate over a BRST quartet and arrive at the well known formula of MNS. Thesis submitted for the Degree of Doctor of Philosophy in the University of Oxford
Covariant Field Equations, Gauge Fields and Conservation Laws from YangMills Matrix Models
, 2008
"... The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in YangMills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as YangMills algebra. Remarkably, the equations of moti ..."
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Cited by 20 (17 self)
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The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in YangMills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as YangMills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the wouldbe topological term. In particular, the IKKT matrix model is capable of describing 4dimensional NC spacetimes with a general effective metric. Metric deformations of flat MoyalWeyl space are briefly discussed.
Curvedspace classical solutions of a massive supermatrix model
 Nucl. Phys. B
"... We investigate here a supermatrix model with a mass term and a cubic interaction. It is based on the super Lie algebra osp(132, R), which could play a rôle in the construction of the elevendimensional Mtheory. This model contains a massive version of the IIB matrix model, where some fields have a ..."
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Cited by 18 (1 self)
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We investigate here a supermatrix model with a mass term and a cubic interaction. It is based on the super Lie algebra osp(132, R), which could play a rôle in the construction of the elevendimensional Mtheory. This model contains a massive version of the IIB matrix model, where some fields have a tachyonic mass term. Therefore, the trivial vacuum of this theory is unstable. However, this model possesses several classical solutions where these fields build noncommutative curved spaces and these solutions are shown to be energetically more favorable than the trivial vacuum. In particular, we describe in details two cases, the SO(3)×SO(3)×SO(3) (three fuzzy 2spheres) and the SO(9) (fuzzy 8sphere) classical backgrounds.
Gaussian and mean field approximations for reduced YangMills integrals
 JHEP 0103, 026 (2001) [hepth/0011175]; F. Sugino, Gaussian and
"... In this paper, we consider bosonic reduced YangMills integrals by using some approximation schemes, which are a kind of mean field approximation called Gaussian approximation and its improved version. We calculate the free energy and the expectation values of various operators including Polyakov lo ..."
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Cited by 17 (6 self)
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In this paper, we consider bosonic reduced YangMills integrals by using some approximation schemes, which are a kind of mean field approximation called Gaussian approximation and its improved version. We calculate the free energy and the expectation values of various operators including Polyakov loop and Wilson loop. Our results nicely match to the exact and the numerical results obtained before. Quite good scaling behaviors of the Polyakov loop and of the Wilson loop can be seen under the ’t Hooft like large N limit for the case of the loop length smaller. Then, simple analytic expressions for the loops are obtained. Furthermore, we compute the Polyakov loop and the Wilson loop for the case of the loop length sufficiently large, where with respect to the Polyakov loop there seems to be no known results in appropriate literatures even in numerical calculations. The result of the Wilson loop exhibits a strong resemblance to the result simulated for a few smaller values of N in the supersymmetric case.
Adding a Myers term to the IIB matrix model
 JHEP
, 2003
"... Preprint typeset in JHEP style HYPER VERSION ..."
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