91 research outputs found
Running couplings in equivariantly gauge-fixed SU(N) Yang--Mills theories
In equivariantly gauge-fixed SU(N) Yang--Mills theories, the gauge symmetry
is only partially fixed, leaving a subgroup unfixed. Such
theories avoid Neuberger's nogo theorem if the subgroup contains at least
the Cartan subgroup , and they are thus non-perturbatively well
defined if regulated on a finite lattice. We calculate the one-loop beta
function for the coupling , where is the gauge
coupling and is the gauge parameter, for a class of subgroups including
the cases that or . The
coupling represents the strength of the interaction of the gauge
degrees of freedom associated with the coset . We find that
, like , is asymptotically free. We solve the
renormalization-group equations for the running of the couplings and
, and find that dimensional transmutation takes place also for the
coupling , generating a scale which can be larger
than or equal to the scale associated with the gauge coupling ,
but not smaller. We speculate on the possible implications of these results.Comment: 14 pages, late
Phase switching in a voltage-biased Aharonov-Bohm interferometer
Recent experiment [Sigrist et al., Phys. Rev. Lett. {\bf 98}, 036805 (2007)]
reported switches between 0 and in the phase of Aharonov-Bohm
oscillations of the two-terminal differential conductance through a two-dot
ring with increasing voltage bias. Using a simple model, where one of the dots
contains multiple interacting levels, these findings are explained as a result
of transport through the interferometer being dominated at different biases by
quantum dot levels of different "parity" (i.e. the sign of the overlap integral
between the dot state and the states in the leads). The redistribution of
electron population between different levels with bias leads to the fact that
the number of switching events is not necessarily equal to the number of dot
levels, in agreement with experiment. For the same reason switching does not
always imply that the parity of levels is strictly alternating. Lastly, it is
demonstrated that the correlation between the first switching of the phase and
the onset of the inelastic cotunneling, as well as the sharp (rather than
gradual) change of phase when switching occurs, give reason to think that the
present interpretation of the experiment is preferable to the one based on
electrostatic AB effect.Comment: 12 pages, 9 figure
Chiral Transition of SU(4) Gauge Theory with Fermions in Multiple Representations
We report preliminary results on the finite temperature behavior of SU(4)
gauge theory with dynamical quarks in both the fundamental and two-index
antisymmetric representations. This system is a candidate to present scale
separation behavior, where fermions in different representations condense at
different temperature or coupling scales. Our simulations, however, reveal a
single finite-temperature phase transition at which both representations
deconfine and exhibit chiral restoration. It appears to be strongly first
order. We compare our results to previous single-representation simulations. We
also describe a Pisarski-Wilczek stability analysis, which suggests that the
transition should be first order.Comment: 8 pages, 5 figures. Presented at at Lattice 2017, the 35th
International Symposium on Lattice Field Theory, Granada, Spain, 18-24 June
201
Spin-Orbit-Induced Magnetic Anisotropy for Impurities in Metallic Samples I. Surface Anisotropy
Motivated by the recent measurements of Kondo resistivity in thin films and
wires, where the Kondo amplitude is suppressed for thinner samples, the surface
anisotropy for magnetic impurities is studied. That anisotropy is developed in
those cases where in addition to the exchange interaction with the impurity
there is strong spin-orbit interaction for conduction electrons around the
impurity in the ballistic region. The asymmetry in the neighborhood of the
magnetic impurity exhibits the anisotropy axis which, in the case of a
plane surface, is perpendicular to the surface. The anisotropy energy is
for spin , and the anisotropy constant is
inversionally proportional to distance measured from the surface and
. Thus at low temperature the spin is frozen in a singlet or doublet of
lowest energy. The influence of that anisotropy on the electrical resistivity
is the subject of the following paper (part II).Comment: 28 pages, RevTeX (using epsfig), 8 eps figures included, submitted to
PR
Constraints on the Existence of Chiral Fermions in Interacting Lattice Theories
It is shown that an interacting theory, defined on a regular lattice, must
have a vector-like spectrum if the following conditions are satisfied:
(a)~locality, (b)~relativistic continuum limit without massless bosons, and
(c)~pole-free effective vertex functions for conserved currents.
The proof exploits the zero frequency inverse retarded propagator of an
appropriate set of interpolating fields as an effective quadratic hamiltonian,
to which the Nielsen-Ninomiya theorem is applied.Comment: LaTeX, 9 pages, WIS--93/56--JUNE--P
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