Spontaneous breaking of the rotational symmetry in dimensionally reduced super Yang-Mills models

Abstract

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) \to 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.

arXiv comment27 pages, 14 figures

Cited by in corpus (13)

• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
• Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Progress in the numerical studies of the type IIB matrix model
• Emergent Metric Space-Time from Matrix Theory
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models
• A practical solution to the sign problem in a matrix model for dynamical compactification
• Critical Dimension and Negative Specific Heat in One-dimensional Large-N Reduced Models
• A renormalization group method for studying the early universe in the Lorentzian IIB matrix model
• A Renormalization Group Approach to A Yang-Mills Two Matrix Model
• (3+1)-dimensional expanding universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions
• Recent developments in the type IIB matrix model