Dynamical consequences of 1-form symmetries and the exceptional Argyres-Douglas theories

Abstract

Higher-form symmetries have proved useful in constraining the dynamics of a number of quantum field theories. In the context of the Argyres-Douglas (AD) theories of the (G, G ) type, we find that the 1-form symmetries are invariant under the Higgs branch flow, and that they are captured by the non-Higgsable sector at a generic point on the Higgs branch of the AD theory in question. As a consequence, dimensional reduction of an AD theory with a non-trivial 1-form symmetry to 3d leads to a free sector. We utilize these observations, along with other results, to propose systematically the mirror theories for the AD theories of the (A n , E m ) type. As a by-product of these findings, we discover many important results: the Flip-Flip duality for all T [G] theories with simply-laced group G, including the exceptional ones; the class S descriptions of exceptional affine Dynkin diagram such that all gauge groups are special unitary; the universality of the mirror theories for D h ∨ G (G) with h ∨ G the dual Coxeter number of G; and the triviality of the 2-group structure in the (A n , E m ) theories.

Dirac pairings, one-form symmetries and Seiberg-Witten geometries

“…In particular, an immediate implication of the known classification of rank-1 Coulomb branch geometries [21][22][23][24] is that since -with one exception -all have only principally polarized homology lattices, it follows that all rank-1 SCFTs have principal Dirac pairings, their charge and line lattices coincide, and they have no 1form symmetries. This agrees with the predictions from string constructions and BPS quivers [11][12][13][14][15][16][17][18][19][20]. The one exception is the Coulomb branch geometry of the N =2 * su(2) sYM theory which also has a model with non-principally polarized homology lattice, which is consistent with the field theory expectation.…”

“…In this work we only apply our analysis to re-derive the global structures and one-form symmetries of N = 4 sYM theories as examples, but our techniques apply more generally to N = 2 theories for which many results are by now known [11][12][13][14][15][16][17][18][19][20]. In particular, an immediate implication of the known classification of rank-1 Coulomb branch geometries [21][22][23][24] is that since -with one exception -all have only principally polarized homology lattices, it follows that all rank-1 SCFTs have principal Dirac pairings, their charge and line lattices coincide, and they have no 1form symmetries.…”