Effective actions of matrix models on homogeneous spaces

Imai, Takaaki; Kitazawa, Yoshihisa; Takayama, Yastoshi; Tomino, Dan

doi:10.1016/j.nuclphysb.2003.11.038

Cited by 50 publications

(78 citation statements)

References 27 publications

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“…Quantum corrections in gauge theories on these spaces are investigated in [24,25,26,27,28]. The symmetric trace of the operators on a compact space is defined as…”

Section: Wilson Line Correlators In Noncommutative Gauge Theorymentioning

confidence: 99%

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Graviton propagators in supergravity and noncommutative gauge theory

Kitazawa

Nagaoka

2007

Phys. Rev. D

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We investigate the graviton propagator in the type IIB supergravity background which is dual to 4 dimensional noncommutative gauge theory. We assume that the boundary is located not at the infinity but at the noncommutative scale where the string frame metric exhibits the maximum. We argue that the Neumann boundary condition is the appropriate boundary condition to be adopted at the boundary. We find that the graviton propagator behaves just as that of the 4 dimensional massless graviton. On the other hand, the non-analytic behaviors of the other Kaluza-Klein modes are not significantly affected by the Neumann boundary condition.

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“…Quantum corrections in gauge theories on these spaces are investigated in [24,25,26,27,28]. The symmetric trace of the operators on a compact space is defined as…”

Section: Wilson Line Correlators In Noncommutative Gauge Theorymentioning

confidence: 99%

“…H (i) are related with Floquet solutions J(ν, z) as 25) and J(ν, z) is expanded in terms of Bessel functions as…”

Section: Graviton Modesmentioning

confidence: 99%

Graviton propagators in supergravity and noncommutative gauge theory

Kitazawa

Nagaoka

2007

Phys. Rev. D

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“…Further evidence for the emergence of a four-dimensional space-time based on perturbative calculations around fuzzy-sphere like solutions is provided in Ref. 8).…”

Section: §1 Introductionmentioning

confidence: 99%

Gaussian Expansion Analysis of a Matrix Model with the Spontaneous Breakdown of Rotational Symmetry

Nishimura

Okubo

Sugino

2005

Progress of Theoretical Physics

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Recently, the Gaussian expansion method has been applied to investigate the dynamical generation of 4d space-time in the IIB matrix model, which is a conjectured nonperturbative definition of type IIB superstring theory in 10 dimensions. Evidence for such a phenomenon, which is associated with the spontaneous breaking of the SO(10) symmetry down to SO(4), has been obtained up to 7-th order calculations. Here we apply the same method to a simplified model, which is considered to exhibit an analogous spontaneous symmetry breaking via the same mechanism as conjectured for the IIB matrix model. The results up to 9-th order demonstrate a clear convergence, which allows us to unambiguously identify the actual symmetry breaking pattern by comparing the free energy of possible vacua and to calculate the extent of "space-time" in each direction. §1. IntroductionIt has long been believed that matrix models may be useful as a nonperturbative formulation of string theory, and hence play an important role similar to the lattice formulation of quantum field theory. Indeed, matrix models have been quite successful in formulating non-critical string theory, and after the development of such notions as string duality and D-branes, the idea has been extended also to critical strings. The IIB matrix model 1) is one such proposal, which is conjectured to be a nonperturbative definition of type IIB superstring theory in 10 dimensions. It is a supersymmetric matrix model, which can be formally obtained as the zero-volume limit of 10d SU (N ) super Yang-Mills theory.In this model space-time is represented by the eigenvalue distribution of ten bosonic matrices. 2) If the distribution collapses dynamically to a four-dimensional hypersurface, which, in particular, requires the SO(10) symmetry of the model to be spontaneously broken, we may naturally understand the dimensionality of our space-time as a result of the nonperturbative dynamics of superstring theory. In Ref.3) the first evidence for the above scenario was obtained by calculating the free * ) 488 J. Nishimura, T. Okubo and F. Sugino energy of space-times with various dimensionalities using the Gaussian expansion method up to 3rd order. Higher-order calculations, 4), 5) as well as tests of the method itself in simpler models, 6), 7) have strengthened the conclusion considerably. Further evidence for the emergence of a four-dimensional space-time based on perturbative calculations around fuzzy-sphere like solutions is provided in Ref. 8).While these results are certainly encouraging, it is desirable to understand the mechanism responsible for the spontaneous symmetry breaking (SSB) of rotational symmetry. In Ref. 9) it is pointed out that the phase of the fermion determinant favors lower-dimensional configurations, since the phase becomes stationary around such configurations. * ) Indeed, Monte Carlo simulations show that SSB does not occur in various models without such a phase factor. 12)-14) Unfortunately, including the effects of the phase in Monte Carlo simulations is techni...

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“…In fact there are certain evidences in the IIB matrix model [2] that fourdimensional space-time is generated dynamically [5][6][7][8]. In refs.…”

Section: Introductionmentioning

confidence: 99%

Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres

Anagnostopoulos

Azuma

Nagao

et al. 2005

J. High Energy Phys.

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We study a 4d supersymmetric matrix model with a cubic term, which incorporates fuzzy spheres as classical solutions, using Monte Carlo simulations and perturbative calculations. The fuzzy sphere in the supersymmetric model turns out to be always stable if the large-N limit is taken in such a way that various correlation functions scale. This is in striking contrast to analogous bosonic models, where the fuzzy sphere decays into the pure Yang-Mills vacuum due to quantum effects when the coefficient of the cubic term becomes smaller than a critical value. We also find that the power-law tail of the eigenvalue distribution, which exists in the supersymmetric model without the cubic term, disappears in the presence of the fuzzy sphere in the large-N limit. Coincident fuzzy spheres turn out to be unstable, which implies that the dynamically generated gauge group is U(1).

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Effective actions of matrix models on homogeneous spaces

Cited by 50 publications

References 27 publications

Graviton propagators in supergravity and noncommutative gauge theory

Graviton propagators in supergravity and noncommutative gauge theory

Gaussian Expansion Analysis of a Matrix Model with the Spontaneous Breakdown of Rotational Symmetry

Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres

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