768 research outputs found
Unitary One Matrix Models: String Equations and Flows
We review the Symmetric Unitary One Matrix Models. In particular we discuss
the string equation in the operator formalism, the mKdV flows and the Virasoro
Constraints. We focus on the \t-function formalism for the flows and we
describe its connection to the (big cell of the) Sato Grassmannian \Gr via
the Plucker embedding of \Gr into a fermionic Fock space. Then the space of
solutions to the string equation is an explicitly computable subspace of
\Gr\times\Gr which is invariant under the flows.Comment: 20 pages (Invited talk delivered by M. J. Bowick at the Vth Regional
Conference on Mathematical Physics, Edirne Turkey: December 15-22, 1991.
Abelian gauge fields coupled to simplicial quantum gravity
We study the coupling of Abelian gauge theories to four-dimensional
simplicial quantum gravity. The gauge fields live on dual links. This is the
correct formulation if we want to compare the effect of gauge fields on
geometry with similar effects studied so far for scalar fields. It shows that
gauge fields couple equally weakly to geometry as scalar fields, and it offers
an understanding of the relation between measure factors and Abelian gauge
fields observed so-far.Comment: 20 page
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
Singularities of the Partition Function for the Ising Model Coupled to 2d Quantum Gravity
We study the zeros in the complex plane of the partition function for the
Ising model coupled to 2d quantum gravity for complex magnetic field and real
temperature, and for complex temperature and real magnetic field, respectively.
We compute the zeros by using the exact solution coming from a two matrix model
and by Monte Carlo simulations of Ising spins on dynamical triangulations. We
present evidence that the zeros form simple one-dimensional curves in the
complex plane, and that the critical behaviour of the system is governed by the
scaling of the distribution of the singularities near the critical point.
Despite the small size of the systems studied, we can obtain a reasonable
estimate of the (known) critical exponents.Comment: 22 pages, LaTeX2e, 10 figures, added discussion on antiferromagnetic
transition and reference
The Concept of Time in 2D Quantum Gravity
We show that the ``time'' t_s defined via spin clusters in the Ising model
coupled to 2d gravity leads to a fractal dimension d_h(s) = 6 of space-time at
the critical point, as advocated by Ishibashi and Kawai. In the unmagnetized
phase, however, this definition of Hausdorff dimension breaks down. Numerical
measurements are consistent with these results. The same definition leads to
d_h(s)=16 at the critical point when applied to flat space. The fractal
dimension d_h(s) is in disagreement with both analytical prediction and
numerical determination of the fractal dimension d_h(g), which is based on the
use of the geodesic distance t_g as ``proper time''. There seems to be no
simple relation of the kind t_s = t_g^{d_h(g)/d_h(s)}, as expected by
dimensional reasons.Comment: 14 pages, LaTeX, 2 ps-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
Large Gauged Q Balls
We study Q-balls associated with local U(1) symmetries. Such Q-balls are expected to become unstable for large values of their charge because of the repulsion mediated by the gauge force. We consider the possibility that the repulsion is eliminated through the presence in the interior of the Q-ball of fermions with charge opposite to that of the scalar condensate. Another possibility is that two scalar condensates of opposite charge form in the interior. We demonstrate that both these scenaria can lead to the existence of classically stable, large, gauged Q-balls. We present numerical solutions, as well as an analytical treatment of the ``thin-wall'' limit
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