1,470 research outputs found
Expansion of Two-Dimensional Models in the Scaling Region
The main technical and conceptual features of the lattice expansion in
the scaling region are discussed in the context of a two-parameter
two-dimensional spin model interpolating between and
models, with standard and improved lattice actions. We show how to
perform the asymptotic expansion of effective propagators for small values of
the mass gap and how to employ this result in the evaluation of physical
quantities in the scaling regime. The lattice renormalization group
function is constructed explicitly and exactly to .Comment: 6 pages, report no. IFUP-TH 49/9
A solvable twisted one-plaquette model
We solve a hot twisted Eguchi-Kawai model with only timelike plaquettes in
the deconfined phase, by computing the quadratic quantum fluctuations around
the classical vacuum. The solution of the model has some novel features: the
eigenvalues of the time-like link variable are separated in L bunches, if L is
the number of links of the original lattice in the time direction, and each
bunch obeys a Wigner semicircular distribution of eigenvalues. This solution
becomes unstable at a critical value of the coupling constant, where it is
argued that a condensation of classical solutions takes place. This can be
inferred by comparison with the heat-kernel model in the hamiltonian limit, and
the related Douglas-Kazakov phase transition in QCD2. As a byproduct of our
solution, we can reproduce the dependence of the coupling constant from the
parameter describing the asymmetry of the lattice, in agreement with previous
results by Karsch.Comment: Minor corrections; final version to appear on IJMPA. 22 pages, Latex,
2 (small) figures included with eps
Analytic results in 2+1-dimensional Finite Temperature LGT
In a 2+1-dimensional pure LGT at finite temperature the critical coupling for
the deconfinement transition scales as , where
is the number of links in the ``time-like'' direction of the symmetric
lattice. We study the effective action for the Polyakov loop obtained by
neglecting the space-like plaquettes, and we are able to compute analytically
in this context the coefficient for any SU(N) gauge group; the value of
is instead obtained from the effective action by means of (improved) mean
field techniques. Both coefficients have already been calculated in the large N
limit in a previous paper. The results are in very good agreement with the
existing Monte Carlo simulations. This fact supports the conjecture that, in
the 2+1-dimensional theory, space-like plaquettes have little influence on the
dynamics of the Polyakov loops in the deconfined phase.Comment: 15 pages, Latex, 2 figures included with eps
An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry -Summary of the Formulation-
We propose a lattice field theory formulation which overcomes some
fundamental difficulties in realizing exact supersymmetry on the lattice. The
Leibniz rule for the difference operator can be recovered by defining a new
product on the lattice, the star product, and the chiral fermion species
doublers degrees of freedom can be avoided consistently. This framework is
general enough to formulate non-supersymmetric lattice field theory without
chiral fermion problem. This lattice formulation has a nonlocal nature and is
essentially equivalent to the corresponding continuum theory. We can show that
the locality of the star product is recovered exponentially in the continuum
limit. Possible regularization procedures are proposed.The associativity of the
product and the lattice translational invariance of the formulation will be
discussed.Comment: 14 pages, Lattice2017 Proceeding
Twisted N=2 exact SUSY on the lattice for BF and Wess-Zumino
We formulate exact supersymmetric models on a lattice. We introduce
noncommutativity to ensure the Leibniz rule. With the help of superspace
formalism, we give supertransformations which keep the N=2 twisted SUSY algebra
exactly. The action is given as a product of (anti)chiral superfields on the
lattice. We present BF and Wess-Zumino models as explicit examples of our
formulation. Both models have exact N=2 twisted SUSY in 2 dimensional space at
a finite lattice spacing. In component fields, the action has supercharge exact
form.Comment: 3 pages, 2 figures, talk presented by I. Kanamori at
Lattice2004(Theory), Fermilab, 21-26 June 200
An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry
We propose an unconventional formulation of lattice field theories which is
quite general, although originally motivated by the quest of exact lattice
supersymmetry. Two long standing problems have a solution in this context: 1)
Each degree of freedom on the lattice corresponds to degrees of freedom
in the continuum, but all these doublers have (in the case of fermions) the
same chirality and can be either identified, thus removing the degeneracy, or,
in some theories with extended supersymmetry, identified with different members
of the same supermultiplet. 2) The derivative operator, defined on the lattice
as a suitable periodic function of the lattice momentum, is an addittive and
conserved quantity, thus assuring that the Leibnitz rule is satisfied. This
implies that the product of two fields on the lattice is replaced by a
non-local "star product" which is however in general non-associative.
Associativity of the "star product" poses strong restrictions on the form of
the lattice derivative operator (which becomes the inverse gudermannian
function of the lattice momentum) and has the consequence that the degrees of
freedom of the lattice theory and of the continuum theory are in one-to-one
correspondence, so that the two theories are eventually equivalent.
Regularization of the ultraviolet divergences on the lattice is not associated
to the lattice spacing, which does not act as a regulator, but may be obtained
by a one parameter deformation of the lattice derivative, thus preserving the
lattice structure even in the limit of infinite momentum cutoff. However this
regularization breaks gauge invariance and a gauge invariant regularization
within the lattice formulation is still lacking.Comment: 68 pages, 7 figure
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