8,814 research outputs found
Ginsparg-Wilson Fermions in Odd Dimensions
The Ginsparg-Wilson relation, if written in a suitable form, can be used as a
condition for lattice Dirac operators of massless fermions also in odd
dimensions. The fermion action with such a Dirac operator is invariant under a
generalized parity transformation, which reduces to the ordinary parity
transformation in the (naive) continuum limit. The fermion measure, however,
transforms non-trivially under the generalized parity transformation, and hence
the parity anomaly arises solely from the fermion measure. The analogy to the
lattice construction of chiral gauge theories in even dimensions is clarified
by considering a dimensional reduction. We also propose a natural definition of
a lattice Chern-Simons term, which is consistent with odd dimensional
Ginsparg-Wilson fermions.Comment: 15 pages, no figures, final version published in JHE
The continuum limit of the non-commutative lambda phi^4 model
We present a numerical study of the \lambda \phi^{4} model in three Euclidean
dimensions, where the two spatial coordinates are non-commutative (NC). We
first show the explicit phase diagram of this model on a lattice. The ordered
regime splits into a phase of uniform order and a ``striped phase''. Then we
discuss the dispersion relation, which allows us to introduce a dimensionful
lattice spacing. Thus we can study a double scaling limit to zero lattice
spacing and infinite volume, which keeps the non-commutativity parameter
constant. The dispersion relation in the disordered phase stabilizes in this
limit, which represents a non-perturbative renormalization. From its shape we
infer that the striped phase persists in the continuum, and we observe UV/IR
mixing as a non-perturbative effect.Comment: 3 pages, 3 figures, talk presented by W.B. at the 11th Regional
Conference on Mathematical Physics, Tehran, May 3-6, 200
Non--Commutative Field Theories beyond Perturbation Theory
We investigate two models in non-commutative (NC) field theory by means of
Monte Carlo simulations. Even if we start from the Euclidean lattice
formulation, such simulations are only feasible after mapping the systems onto
dimensionally reduced matrix models. Using this technique, we measure Wilson
loops in 2d NC gauge theory of rank 1. It turns out that they are
non-perturbatively renormalizable, and the phase follows an Aharonov-Bohm
effect if we identify \theta = 1/B. Next we study the 3d \lambda \phi^{4} model
with two NC coordinates, where we present new results for the correlators and
the dispersion relation. We further reveal the explicit phase diagram. The
ordered regime splits into a uniform and a striped phase, as it was
qualitatively conjectured before. We also confirm the recent observation by
Ambjorn and Catterall that such stripes occur even in d=2, although they imply
the spontaneous breaking of translation symmetry. However, in d=3 and d=2 we
observe only patterns of two stripes to be stable in the range of parameters
investigated.Comment: 8 pages, 8 figures, talk presented at 35th Ahrenshoop Symposiu
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
A non-perturbative study of non-commutative U(1) gauge theory
We study U(1) gauge theory on a 4d non-commutative torus, where two
directions are non-commutative. Monte Carlo simulations are performed after
mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At
intermediate coupling strength, we find a phase in which open Wilson lines
acquire non-zero vacuum expectation values, which implies the spontaneous
breakdown of translational invariance. In this phase, various physical
quantities obey clear scaling behaviors in the continuum limit with a fixed
non-commutativity parameter theta, which provides evidence for a possible
continuum theory. In the weak coupling symmetric phase, the dispersion relation
involves a negative IR-singular term, which is responsible for the observed
phase transition.Comment: 7 pages, 4 figures, Talk presented by J. Nishimura at the 21st
Nishinomiya-Yukawa Memorial Symposium on Theoretical Physics:
``Noncommutative Geometry and Quantum Spacetime in Physics'', Nishinomiya and
Kyoto (2006
On the Quantum Geometry of String Theory
The IKKT or IIB matrix model has been proposed as a non-perturbative
definition of type IIB superstring theories. It has the attractive feature that
space--time appears dynamically. It is possible that lower dimensional
universes dominate the theory, therefore providing a dynamical solution to the
reduction of space--time dimensionality. We summarize recent works that show
the central role of the phase of the fermion determinant in the possible
realization of such a scenario.Comment: 3 pages, 2 figures, Lattice2001(surfaces
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