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Model of supersymmetric quantum field theory with broken parity symmetry
Recently, it was observed that self-interacting scalar quantum field theories
having a non-Hermitian interaction term of the form ,
where is a real positive parameter, are physically acceptable in the
sense that the energy spectrum is real and bounded below. Such theories possess
PT invariance, but they are not symmetric under parity reflection or time
reversal separately. This broken parity symmetry is manifested in a nonzero
value for , even if is an even integer. This paper extends
this idea to a two-dimensional supersymmetric quantum field theory whose
superpotential is . The resulting quantum
field theory exhibits a broken parity symmetry for all . However,
supersymmetry remains unbroken, which is verified by showing that the
ground-state energy density vanishes and that the fermion-boson mass ratio is
unity.Comment: 20 pages, REVTeX, 11 postscript figure
Distinguished bases of exceptional modules
Exceptional modules are tree modules. A tree module usually has many tree
bases and the corresponding coefficient quivers may look quite differently. The
aim of this note is to introduce a class of exceptional modules which have a
distinguished tree basis, we call them radiation modules (generalizing an
inductive construction considered already by Kinser). For a Dynkin quiver,
nearly all indecomposable representations turn out to be radiation modules, the
only exception is the maximal indecomposable module in case E_8. Also, the
exceptional representation of the generalized Kronecker quivers are given by
radiation modules. Consequently, with the help of Schofield induction one can
display all the exceptional modules of an arbitrary quiver in a nice way.Comment: This is a revised and slightly expanded version. Propositions 1 and 2
have been corrected, some examples have been inserte
Flavor mixing in a Lee-type model
An exactly solvable Quantum Field Theory (QFT) model of Lee-type is
constructed to study how neutrino flavor eigenstates are created through
interactions and how the localization properties of neutrinos follows from the
parent particle that decays. The two-particle states formed by the neutrino and
the accompanying charged lepton can be calculated exactly as well as their
creation probabilities. We can show that the coherent creation of neutrino
flavor eigenstates follows from the common negligible contribution of neutrino
masses to their creation probabilities. On the other hand, it is shown that it
is not possible to associate a well defined "flavor" to mixed states of charged
leptons.Comment: v2: 25pp in preprint form, typos corrected and references added, one
paragraph around Eq.(90) added in conclusion
Dimensional effects on the tunneling conductivity of gold-implanted nanocomposite films
We study the dependence of the electrical conductivity on the gold
concentration of Au-implanted polymethylmethacrylate (PMMA) and alumina
nanocomposite thin films. For Au contents larger than a critical concentration,
the conductivity of Au-PMMA and Au-alumina is well described by percolation in
two dimensions, indicating that the critical correlation length for percolation
is larger than the thickness of the films. Below the critical loading, the
conductivity is dominated by tunneling processes between isolated Au particles
dispersed in PMMA or alumina continuous matrices. Using an effective medium
analysis of the tunneling conductivity, we show that Au-PMMA behaves as a
tunneling system in two dimensions, as the film thickness is comparable to the
mean Au particle size. On the contrary, the conductivity of Au-alumina films is
best described by tunneling in three dimensions, although the film thickness is
only a few times larger than the particle size. We interpret the enhancement of
the effective dimensionality of Au-alumina films in the tunneling regime as due
to the larger film thickness as compared to the mean interparticle distances.Comment: 7 pages, 7 figure
New Gauged N=8, D=4 Supergravities
New gaugings of four dimensional N=8 supergravity are constructed, including
one which has a Minkowski space vacuum that preserves N=2 supersymmetry and in
which the gauge group is broken to . Previous gaugings used the
form of the ungauged action which is invariant under a rigid symmetry
and promoted a 28-dimensional subgroup ( or the
non-semi-simple contraction ) to a local gauge group. Here, a
dual form of the ungauged action is used which is invariant under
instead of and new theories are obtained by gauging 28-dimensional
subgroups of . The gauge groups are non-semi-simple and are different
real forms of the groups, denoted , and the new
theories have a rigid SU(2) symmetry. The five dimensional gauged N=8
supergravities are dimensionally reduced to D=4. The gauge
theories reduce, after a duality transformation, to the
gauging while the gauge theory reduces to the gauge
theory. The new theories are related to the old ones via an analytic
continuation. The non-semi-simple gaugings can be dualised to forms with
different gauge groups.Comment: 33 pages. Reference adde
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