612 research outputs found
4D ensembles of percolating center vortices and chains
In this work, we review a recently proposed measure to compute center-element
averages in a mixed ensemble of center vortices and chains with non-Abelian
d.o.f. and monopole fusion. When center vortices percolate and monopoles
condense, the average is captured by a saddle point and collective modes in a
YMH model. In this manner, the L\"uscher term, confining flux tubes with
N-ality and confined gluons were accommodated in an ensemble picture.Comment: 9 pages, 6 figures. Talk presented at the "XIII Quark Confinement and
the Hadron Spectrum" conference (Confinement 2018), 31 July - 6 August 2018,
Maynooth University, Irelan
Effective theory of the D = 3 center vortex ensemble
By means of lattice calculations, center vortices have been established as
the infrared dominant gauge field configurations of Yang-Mills theory. In this
work, we investigate an ensemble of center vortices in D = 3 Euclidean
space-time dimension where they form closed flux loops. To account for the
properties of center vortices detected on the lattice, they are equipped with
tension, stiffness and a repulsive contact interaction. The ensemble of
oriented center vortices is then mapped onto an effective theory of a complex
scalar field with a U(1) symmetry. For a positive tension, small vortex loops
are favoured and the Wilson loop displays a perimeter law while for a negative
tension, large loops dominate the ensemble. In this case the U(1) symmetry of
the effective scalar field theory is spontaneously broken and the Wilson loop
shows an area law. To account for the large quantum fluctuations of the
corresponding Goldstone modes, we use a lattice representation, which results
in an XY model with frustration, for which we also study the Villain
approximation.Comment: 23 page
Non Abelian structures and the geometric phase of entangled qudits
In this work, we address some important topological and algebraic aspects of
two-qudit states evolving under local unitary operations. The projective
invariant subspaces and evolutions are connected with the common elements
characterizing the su(d) Lie algebra and their representations. In particular,
the roots and weights turn out to be natural quantities to parametrize cyclic
evolutions and fractional phases. This framework is then used to recast the
coset contribution to the geometric phase in a form that generalizes the usual
monopole-like formula for a single qubit.Comment: 22 pages, LaTe
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