Monte Carlo Studies of the Dimensionally Reduced 4d SU(N) Super Yang-Mills Theory

We simulate a supersymmetric matrix model obtained from dimensional reduction of 4d SU(N) super Yang-Mills theory. The model is well defined for finite N and it is found that the large N limit obtained by keeping g^2 N fixed gives rise to well defined operators which represent string amplitudes. The space-time structure which arises dynamically from the eigenvalues of the bosonic matrices is discussed, as well as the effect of supersymmetry on the dynamical properties of the model. Eguchi-Kawai equivalence of this model to ordinary gauge theory does hold within a finite range of scale. We report on new simulations of the bosonic model for N up to 768 that confirm this property, which comes as a surprise since no quenching or twist is introduced.Comment: 6 pages, 7 figures, Talk presented by K.N.A. at the HEP 2000 Annual Workshop of the Hellenic Society for the Study of High Energy Physics at the University of Ioannina. References added, minor correction

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 nontrivial 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.Comment: 35 pages, 17 figure

Adaptive epidemic dissemination as a finite-horizon optimal stopping problem

Wireless ad hoc networks are characterized by their limited capabilities and their routine deployment in unfavorable environments. This creates the strong requirement to regulate energy expenditure. We present a scheme to regulate energy cost through optimized transmission scheduling in a noisy epidemic dissemination environment. Building on the intrinsically cross-layer nature of the adaptive epidemic dissemination process, we strive to deliver an optimized mechanism, where energy cost is regulated without compromising the network infection. Improvement of data freshness and applicability in routing are also investigated. Extensive simulations are used to support our proposal

Quantum Geometry and Diffusion

We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from two. We determine the scaling properties of the quantum gravity averaged diffusion kernel.Comment: latex2e, 10 pages, 4 figure

Notes on noncommutative supersymmetric gauge theory on the fuzzy supersphere

In these notes we review Klimcik's construction of noncommutative gauge theory on the fuzzy supersphere. This theory has an exact SUSY gauge symmetry with a finite number of degrees of freedom and thus in principle it is amenable to the methods of matrix models and Monte Carlo numerical simulations. We also write down in this article a novel fuzzy supersymmetric scalar action on the fuzzy supersphere

Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings

We study the properties of the space-time that emerges dynamically from the matrix model for type IIB superstrings in ten dimensions. We calculate the free energy and the extent of space-time using the Gaussian expansion method up to the third order. Unlike previous works, we study the SO(d) symmetric vacua with all possible values of d within the range $2 \le d \le 7$, and observe clear indication of plateaus in the parameter space of the Gaussian action, which is crucial for the results to be reliable. The obtained results indeed exhibit systematic dependence on d, which turns out to be surprisingly similar to what was observed recently in an analogous work on the six-dimensional version of the model. In particular, we find the following properties: i) the extent in the shrunken directions is given by a constant, which does not depend on d; ii) the ten-dimensional volume of the Euclidean space-time is given by a constant, which does not depend on d except for d = 2; iii) The free energy takes the minimum value at d = 3. Intuitive understanding of these results is given by using the low-energy effective theory and some Monte Carlo results.Comment: 33 pages, 10 figures; minor corrections, reference added. arXiv admin note: substantial text overlap with arXiv:1007.088

Stability of Neutral Fermi Balls with Multi-Flavor Fermions

A Fermi ball is a kind of non-topological soliton, which is thought to arise from the spontaneous breaking of an approximate $Z_2$ symmetry and to contribute to cold dark matter. We consider a simple model in which fermion fields with multi-flavors are coupled to a scalar field through Yukawa coupling, and examine how the number of the fermion flavors affects the stability of the Fermi ball against the fragmentation. (1)We find that the Fermi ball is stable against the fragmentation in most cases even in the lowest order thin-wall approximation. (2)We then find that in the other specific cases, the stability is marginal in the lowest order thin-wall approximation, and the next-to-leading order correction determines the stable region of the coupling constants; We examine the simplest case where the total fermion number $N_i$ and the Yukawa coupling constant $G_i$ of each flavor $i$ are common to the flavor, and find that the Fermi ball is stable in the limited region of the parameters and has the broader region for the larger number of the flavors.Comment: 10 pages, 3 eps figures, ReVTeX

Simulating Simplified Versions of the IKKT Matrix Model

We simulate a supersymmetric matrix model obtained from dimensional reduction of 4d SU(N) super Yang-Mills theory (a 4d counter part of the IKKT model or IIB matrix model). The eigenvalue distribution determines the space structure. The measurement of Wilson loop correlators reveals a universal large N scaling. Eguchi-Kawai equivalence may hold in a finite range of scale, which is also true for the bosonic case. We finally report on simulations of a low energy approximation of the 10d IKKT model, where we omit the phase of the Pfaffian and look for evidence for a spontaneous Lorentz symmetry breaking.Comment: 4 pages, talk presented at LATTICE 2000 (Bangalore

A practical solution to the sign problem in a matrix model for dynamical compactification

The matrix model formulation of superstring theory offers the possibility to understand the appearance of 4d space-time from 10d as a consequence of spontaneous breaking of the SO(10) symmetry. Monte Carlo studies of this issue is technically difficult due to the so-called sign problem. We present a practical solution to this problem generalizing the factorization method proposed originally by two of the authors (K.N.A. and J.N.). Explicit Monte Carlo calculations and large-N extrapolations are performed in a simpler matrix model with similar properties, and reproduce quantitative results obtained previously by the Gaussian expansion method. Our results also confirm that the spontaneous symmetry breaking indeed occurs due to the phase of the fermion determinant, which vanishes for collapsed configurations. We clarify various generic features of this approach, which would be useful in applying it to other statistical systems with the sign problem.Comment: 44 pages, 64 figures, v2: some minor typos correcte

High temperature expansion in supersymmetric matrix quantum mechanics

We formulate the high temperature expansion in supersymmetric matrix quantum mechanics with 4, 8 and 16 supercharges. The models can be obtained by dimensionally reducing N=1 U(N) super Yang-Mills theory in D=4,6,10 to 1 dimension, respectively. While the non-zero frequency modes become weakly coupled at high temperature, the zero modes remain strongly coupled. We find, however, that the integration over the zero modes that remains after integrating out all the non-zero modes perturbatively, reduces to the evaluation of connected Green's functions in the bosonic IKKT model. We perform Monte Carlo simulation to compute these Green's functions, which are then used to obtain the coefficients of the high temperature expansion for various quantities up to the next-leading order. Our results nicely reproduce the asymptotic behaviors of the recent simulation results at finite temperature. In particular, the fermionic matrices, which decouple at the leading order, give rise to substantial effects at the next-leading order, reflecting finite temperature behaviors qualitatively different from the corresponding models without fermions.Comment: 17 pages, 13 figures, (v2) some typos correcte