64 research outputs found
Curious patterns of IR symmetry enhancement
We study several cases of IR enhancements of global symmetry in four
dimensions. In particular, we consider a sequence of supersymmetric
gauge theories () with vectors and spinor matter with
components. We show that the subgroup of the flavor symmetry of these theories
rotating the matter in the spinor representations in the UV, when proper gauge
singlet fields are added, enhances to the commutant of in . We
discuss several other interesting cases of enhanced symmetries and the
interplay between symmetry enhancement and self-duality. We also make some
observations about possible interconnections between chiral ring relations and
symmetry enhancement. Finally, we conjecture relations of the discussed models
to compactifications of certain conformal matter models in six dimensions on
tori. The conjecture is based on deriving a relation between five dimensional
models with gauge groups and conformal theories in six dimensions. As a
by product of our considerations we discover a new instance of a simple
self-duality of a theory with an gauge group.Comment: 37 pages + appendices, 5 figure
Exploring Non-Invertible Symmetries in Free Theories
Symmetries corresponding to local transformations of the fundamental fields
that leave the action invariant give rise to (invertible) topological defects,
which obey group-like fusion rules. One can construct more general
(codimension-one) topological defects by specifying a map between
gauge-invariant operators from one side of the defect and such operators on the
other side. In this work, we apply such construction to Maxwell theory in four
dimensions and to the free compact scalar theory in two dimensions. In the case
of Maxwell theory, we show that a topological defect that mixes the field
strength and its Hodge dual can be at most an rotation.
For rational values of the bulk coupling and the -angle we find an
explicit defect Lagrangian that realizes values of the angle
such that is also rational. We further determine the action of
such defects on Wilson and 't Hooft lines and show that they are in general
non-invertible. We repeat the analysis for the free compact scalar in
two dimensions. In this case we find only four discrete maps: the trivial one,
a map , a -duality-like map , and the product of the last two.Comment: 30
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