JHEP12(2019)052
due to the duality we concl u de t hat it enhances in the IR to SU(8). We therefore see that
a duality can be used to infer that the symmetry of a model enhances in the IR, given that
the dual description possesses an enlarged s y mme tr y. The opposite direction might al so be
useful, and in some cases an enhancement of symmetry can suggest a new dual description
in which the enhanced symmetry is manifest in the UV, see [2] for a recent example.
Another, less trivial instance in which certain dualitie s an d mo de l s wi t h sy m me tr y
enhancement are related was di sc us se d in [3, 4] (see also [5]). In this case, we f ocus on
a specific kind of dualities, called “self dualities”, in which the gauge sec tor of the two
theories is the same and they may differ only by gauge invariant fields. The SU(2) Seiberg
duality discussed above is an example for such a duality, in which the two dual theorie s have
the same gauge group and matter in the fundamental representation, and differ only by
the gauge-singlet fields that are coupled to the mesons in the superpotential. As discussed
in [
3, 4], in many cases where two or more model s are self dual it is possible to construct
a closely related theory which is mapped under the duality transformation to itself (i.e.
without any extra gauge-singlet fiel d s) but with a nontrivial action on t he global symmetry.
Then, i n some cases, the duality will act as an additional symmetry operation, resulting
in an enhancement of the symmetry in the IR. In [3] it was shown how the SU(2) self
duality dis cu sse d above leads to a new SU(2) gauge theory in which the UV sym me tr y is
SU(2) × SU(6) × U(1) and it enhances in the IR to E
6
× U(1). The conformal manifol d of
this theory is composed of a single point, at which the duality ac ts as an extra symmetry.
1
Notice that this relation can also be applied in the other direction, and in some c ase s
a model with symmetry enhancement can be used to find a ne w s el f -dual i ty, see [
3, 4] for
explicit examples.
In this paper we will consider a sequence of N = 1 self dualities with Spin(n + 8)
(1 ≤ n ≤ 6) gauge groups, first appeared in [
8], and use it as mentioned above to construct
a new sequence of models with symmetry enhancement. Then, by i d entifying the resulting
pattern of IR symmetries (gi ven in eq. (
3.29)) we will be able to conjecture its origin from
six-dimensional geometric constructions. Explicitly, we will conjecture that the 4d fixed
points along with their enhanced symmetries can be generated through the compactification
of a family of 6d SCFTs on a Riemann surface with fluxes for the global symmetri e s (see [
9–
21] for discussions of such compactifications). The motivation h er e is to see k a physical
explanation for the enhancement, in which these fixed points are viewed as low-energy
effective 4d theories obtained from putting 6d SCFTs on a compact Riemann surface with
fluxes. The 4d IR symmetries are then just the ones inherited from the corresponding 6d
SCFTs (and preserved by the fluxes). This analy si s is analogous to the one pe r for me d
in [
4] for the sequence of self dualities with Spin(n + 4) (1 ≤ n ≤ 8) gauge groups (first
appeared in [
22]), and extends it to the Spin(n + 8) sequence mentioned above. In fac t, we
1
Let us comment that another variant of this kind of relations between dualities and symmetry enhance-
ment has been discussed in [
6, 7]. In this case, one uses two copies of the SU(2) gauge theory (and a suitable
exactly marginal deformation) in order to construct a model which is mapped to itself under the duality
transformation, and in which the symmetry enhances in th e IR. This is different from the construction of [3]
which involves only one copy, and results in an enhancement of the symmetry from SU(8) in the UV to
E
7
× U(1) in the IR.
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