11,425 research outputs found
The Area Law in Matrix Models for Large N QCD Strings
We study the question whether matrix models obtained in the zero volume limit
of 4d Yang-Mills theories can describe large N QCD strings. The matrix model we
use is a variant of the Eguchi-Kawai model in terms of Hermitian matrices, but
without any twists or quenching. This model was originally proposed as a toy
model of the IIB matrix model. In contrast to common expectations, we do
observe the area law for Wilson loops in a significant range of scale of the
loop area. Numerical simulations show that this range is stable as N increases
up to 768, which strongly suggests that it persists in the large N limit. Hence
the equivalence to QCD strings may hold for length scales inside a finite
regime.Comment: 12 pages, 4 figure
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
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 , 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
A new approach to the complex-action problem and its application to a nonperturbative study of superstring theory
Monte Carlo simulations of a system whose action has an imaginary part are
considered to be extremely difficult. We propose a new approach to this
`complex-action problem', which utilizes a factorization property of
distribution functions. The basic idea is quite general, and it removes the
so-called overlap problem completely. Here we apply the method to a
nonperturbative study of superstring theory using its matrix formulation. In
this particular example, the distribution function turns out to be positive
definite, which allows us to reduce the problem even further. Our numerical
results suggest an intuitive explanation for the dynamical generation of 4d
space-time.Comment: 7 pages, 4 figures, PRD version somewhat extended from the original
versio
Supersymetry on the Noncommutative Lattice
Built upon the proposal of Kaplan et.al. [hep-lat/0206109], we construct
noncommutative lattice gauge theory with manifest supersymmetry. We show that
such theory is naturally implementable via orbifold conditions generalizing
those used by Kaplan {\sl et.al.} We present the prescription in detail and
illustrate it for noncommutative gauge theories latticized partially in two
dimensions. We point out a deformation freedom in the defining theory by a
complex-parameter, reminiscent of discrete torsion in string theory. We show
that, in the continuum limit, the supersymmetry is enhanced only at a
particular value of the deformation parameter, determined solely by the size of
the noncommutativity.Comment: JHEP style, 1+22 pages, no figure, v2: two references added, v3:
three more references adde
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