3 research outputs found
Nonlocal regularisation of noncommutative field theories
We study noncommutative field theories, which are inherently nonlocal, using
a Poincar\'e-invariant regularisation scheme which yields an effective,
nonlocal theory for energies below a cut-off scale. After discussing the
general features and the peculiar advantages of this regularisation scheme for
theories defined in noncommutative spaces, we focus our attention onto the
particular case when the noncommutativity parameter is inversely proportional
to the square of the cut-off, via a dimensionless parameter . We work out
the perturbative corrections at one-loop order for a scalar theory with quartic
interactions, where the signature of noncommutativity appears in
-dependent terms. The implications of this approach, which avoids the
problems related to UV-IR mixing, are discussed from the perspective of the
Wilson renormalisation program. Finally, we remark about the generality of the
method, arguing that it may lead to phenomenologically relevant predictions,
when applied to realistic field theories.Comment: 1+11 pages, 6 figures; v2: references added, typos corrected,
conclusions unchange
Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices
We consider a U(2) Yang-Mills theory on M x S_F^2 where M is a Riemannian
manifold and S_F^2 is the fuzzy sphere. Using essentially the representation
theory of SU(2) we determine the most general SU(2)-equivariant gauge field on
M x S_F^2. This allows us to reduce the Yang-Mills theory on M x S_F^2 down to
an abelian Higgs-type model over M. Depending on the enforcement (or
non-enforcement) of a "constraint" term, the latter may (or may not) lead to
the standard critically-coupled abelian Higgs model in the commutative limit,
S_F^2 -> S^2. For M = R^2, we find that the abelian Higgs-type model admits
vortex solutions corresponding to instantons in the original Yang-Mills theory.
Vortices are in general no longer BPS, but may attract or repel according to
the values of parameters.Comment: 20 pages, 2 figure