Tomohiro Hotta

Dynamical aspects of large-N reduced models

Abstract We study the large- N reduced model of D -dimensional Yang-Mills theory with special attention to dynamical aspects related to the eigenvalues of the N × N matrices, which correspond to the space-time coordinates in the IIB matrix model. We first put an upper bound on the extent of space-time by perturbative arguments. We perform a Monte Carlo simulation and show that the upper bound is actually saturated. The relation of our result to the SSB of the U(1) D symmetry in the Eguchi-Kawai model is clarified. We define a quantity which represents the uncertainty of the space-time coordinates and show that it is of the same order as the extent of space-time, which means that a classical space-time picture is maximally broken. We develop a 1/ D expansion, which enables us to calculate correlation functions of the model analytically. The absence of an SSB of the Lorentz invariance is shown by the Monte Carlo simulation as well as by the 1/ D expansion.

Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory

We perform Monte Carlo simulations of a supersymmetric matrix model, which is obtained by dimensional reduction of 4D SU(N) super Yang-Mills theory. The model can be considered as a four-dimensional counterpart of the IIB matrix model. We extract the space-time structure represented by the eigenvalues of bosonic matrices. In particular we compare the large-N behavior of the space-time extent with the result obtained from a low-energy effective theory. We measure various Wilson loop correlators which represent string amplitudes and we observe a non-trivial universal scaling in N. We also observe that the Eguchi-Kawai equivalence to ordinary gauge theory does hold at least within a finite range of scale. Comparison with the results for the bosonic case clarifies the role of supersymmetry in the large-N dynamics. It does affect the multi-point correlators qualitatively, but the Eguchi-Kawai equivalence is observed even in the bosonic case.

Monte Carlo studies of the IIB matrix model at large N

The low-energy 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 ten-dimensional Lorentz invariance. The imaginary part of the effective action, which causes the so-called sign problem in the simulation, is dropped by hand. The extent of the eigenvalue distribution of the bosonic matrices shows a power-law large-N behavior, consistent with a simple branched-polymer prediction. We observe, however, that the eigenvalue distribution becomes more and more isotropic in the ten-dimensional space-time as we increase N. This suggests that if the spontaneous breakdown of Lorentz invariance really occurs in the IIB matrix model, a crucial role must be played by the imaginary part of the effective action.

Dynamical models for light Higgs doublets in supersymmetric grand unified theories

We consider a supersymmetric hypercolor gauge theory with six flavors of (hyper)quarks interacting strongly at the grand unification scale. Dynamical breaking of the grand unified SU(5

Dynamical supersymmetry breaking without messenger gauge interactions

{)}_{\mathrm{}\mathrm{GUT}}

Natural unification with a supersymmetric SO(10)GUT x SO(6)H gauge theory.

produces a massless pair of composite color-triplet states. Use of the missing partner mechanism yields eventually a pair of massless Higgs doublets, giving large masses to the color-triplet partners. We prove that this pair of massless Higgs doublets survives quantum corrections and remains in the low-energy spectrum as long as the supersymmetry is unbroken. Hence this could solve the most serious problem\char22{}doublet-triplet splitting in the grand unified theories. We also show that the dangerous dimension-five operators for nucleon decays are suppressed simultaneously, which makes our model still more attractive. \textcopyright{} 1996 The American Physical Society.

Scaling Behavior in 4D Simplicial Quantum Gravity

We investigate low-energy models of supersymmetry (SUSY) breaking by means of vectorlike gauge theories for dynamical SUSY breaking. It is not necessary to introduce messenger gauge interactions utilized so far to mediate the SUSY breaking to the standard-model sector, which reduces complications in the model building. We also consider various other ways of SUSY-breaking transmission. {copyright} {ital 1997} {ital The American Physical Society}

Natural unification with a supersymmetric SO(10){sub GUT}{times}SO(6){sub {ital H}} gauge theory

We propose a unified model of elementary particles based on a supersymmetric

Nonabelian Duality and Higgs Multiplets in Supersymmetric Grand Unified Theories

\mathrm{SO}{(10)}_{\mathrm{GUT}}\ifmmode\times\else\texttimes\fi{}\mathrm{SO}{(6)}_{H}

Scaling structures in four-dimensional simplicial gravity☆

gauge theory. This model completely achieves natural unification of the strong and electroweak interactions without any fine tunings. The masslessness of Higgs doublets is guaranteed by a chiral