Author:
Buican Matthew,Jiang Hongliang
Abstract
Abstract
We systematically study 4D $$ \mathcal{N} $$
N
= 2 superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in ℂ4. We show that if a theory in this class has no $$ \mathcal{N} $$
N
= 2-preserving exactly marginal deformation (i.e., the theory is isolated as an $$ \mathcal{N} $$
N
= 2 SCFT), then it has no 1-form symmetry. This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the a and c central charges, this condition implies that IHS theories satisfying $$ a<\frac{1}{24}\left(15r+2f\right) $$
a
<
1
24
15
r
+
2
f
and $$ c<\frac{1}{6}\left(3r+f\right) $$
c
<
1
6
3
r
+
f
(where r is the complex dimension of the Coulomb branch, and f is the rank of the continuous 0-form flavor symmetry) have no 1-form symmetry. After reviewing the 1-form symmetries of other classes of theories, we are motivated to conjecture that general interacting 4D $$ \mathcal{N} $$
N
= 2 SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Cited by
28 articles.
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