Monte Carlo studies of the spontaneous rotational symmetry breaking in dimensionally reduced super Yang-Mills models

Abstract

It has long been speculated that the spontaneous symmetry breaking (SSB) of SO(D) occurs in matrix models obtained by dimensionally reducing super Yang-Mills theory in D=6,10 dimensions. In particular, the D=10 case corresponds to the IIB matrix model, which was proposed as a nonperturbative formulation of superstring theory, and the SSB may correspond to the dynamical generation of four-dimensional space-time. Recently, it has been shown by using the Gaussian expansion method that the SSB indeed occurs for D=6 and D=10, and interesting nature of the SSB common to both cases has been suggested. Here we study the same issue from first principles by a Monte Carlo method in the D=6 case. In spite of a severe complex-action problem, the factorization method enables us to obtain various quantities associated with the SSB, which turn out to be consistent with the previous results obtained by the Gaussian expansion method. This also demonstrates the usefulness of the factorization method as a general approach to systems with the complex-action problem or the sign problem.

28 pages, 19 figures, v2 some minor corrections

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Cited by in corpus (13)

• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
• Justification of the complex Langevin method with the gauge cooling procedure
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• On the quantum structure of space-time, gravity, and higher spin in matrix models
• Progress in the numerical studies of the type IIB matrix model
• Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Realizing three generations of the Standard Model fermions in the type IIB matrix model
• The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model
• On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model
• Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model
• Quantum phase transition of high dimensional Yang-Mills theories
• Recent developments in the type IIB matrix model