Spontaneous Breaking of the Rotational Symmetry in Dimensionally Reduced Super Yang-Mills Models(Particles and Fields)

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概要

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• We investigate the spontaneous breaking of the SO(D) symmetry in matrix models, which can be obtained by the zero-volume limit of pure SU(N) super Yang Mills theory in D=6,10 dimensions. The D=10 case corresponds to the IIB matrix model, which was proposed as a non-perturbative formulation of type IIB superstring theory, and the spontaneous breaking corresponds to the dynamical compactification of space-time suggested in that model. First we study the D=6 case by the Gaussian expansion method, which turns out to yield clearer results than the previous results for the D=10 case for certain technical reasons. By comparing the free energy of the SO(d) symmetric vacua for d=2,3,4,5, we conclude that the breaking SO(6)→SO(3) actually occurs. We find that the extent of space-time in the shrunken directions is almost independent of d. In units of this universal scale, the extended directions seem to have large but still finite extents depending on d. We show that these results for the extent of space-time can be explained quantitatively by an argument based on the low-energy effective theory. With these new insights, we reconsider the previous results for the IIB matrix model, and find that they are also consistent with our argument based on the low-energy effective theory. Thus we arrive at comprehensive understanding and some quantitative predictions concerning the nature of the spontaneous symmetry breaking taking place in these models. The space-time picture that emerges from the IIB matrix model and its implication on possible interpretations of the model are also discussed.

• 2011-03-25

著者

• Okubo Toshiyuki

  Faculty Of Science And Technology Meijo University

• Nishimura Jun

  Kek Theory Center High Energy Accelerator Research Organization

• Aoyama Tatsumi

  Kobayashi-maskawa Institute For The Origin Of Particles And The Universe (kmi) Nagoya University

• OKUBO Toshiyuki

  Faculty of Science and Technology, Meijo University

• NISHIMURA Jun

  KEK Theory Center, High Energy Accelerator Research Organization:The Graduate University for Advanced Studies (SOKENDAI)

• NISHIMURA Jun

  High Energy Accelerator Research Organization (KEK):Department of Particle and Nuclear Physics, Graduate University for Advanced Studies (SOKENDAI)

• Aoyama Tatsumi

  Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University

関連論文

• Spontaneous Breaking of the Rotational Symmetry in Dimensionally Reduced Super Yang-Mills Models(Particles and Fields)
• Gaussian Expansion Analysis of a Matrix Model with the Spontaneous Breakdown of Rotational Symmetry(Particles and Fields)
• Understanding the Mechanism for the Spontaneous Breakdown of Rotational Symmetry in the IIB Matrix Model(Frontiers of Quantum Physics)
• Spontaneous Breaking of the Rotational Symmetry in Dimensionally Reduced Super Yang-Mills Models
• Nonperturbative Study of Non-Commutative U(1) Gauge Theory(Field theory, Lattice and Noncommutative space,NONCOMMUTATIVE GEOMETRY AND QUANTUM SPACETIME IN PHYSICS)
• Planar Dominance in Non-Commutative Field Theories at Infinite External Momentum(Particles and Fields)

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