Higher form symmetries of Argyres-Douglas theories

114

210

Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of ‘trinion’ singularities which exhibit these properties. In Type IIB, they give rise to 4d $$ \mathcal{N} $$ N = 2 SCFTs that we call $$ {D}_p^b $$ D p b (G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d $$ \mathcal{N} $$ N = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as ‘ugly’ components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver ‘bad’. We propose a way to redeem the badness of these quivers using a class $$ \mathcal{S} $$ S realization. We also discover new S-dualities between different $$ {D}_p^b $$ D p b (G)-trinions. For instance, a certain E8 gauging of the E8 Minahan-Nemeschansky theory is S-dual to an E8-shaped Lagrangian quiver SCFT.

Section: Jhep05(2021)274mentioning

confidence: 99%

Section: Jhep05(2021)274mentioning

confidence: 99%

5d and 4d SCFTs: canonical singularities, trinions and S-dualities

Closset

Giacomelli

Schäfer‐Nameki

et al. 2021

114

210

“…From a geometric engineering point of view, higher form symmetries were discussed using the M-theory realization of 5d SCFTs on Calabi-Yau threefolds, as well as other M-theory geometric engineering constructions such as G 2 -holonomy compactifications to 4d in [23,27,28]. Related works in Type IIB, for 4d SCFTs in particular Argyres-Douglas theories were obtained in [25,29,30]. In 6d the defect group was analyzed in [31] and the 1-form symmetries in 6d SCFTs were discussed from a geometric construction in [27].…”

Section: Jhep02(2021)159mentioning

confidence: 99%

Higher-form symmetries of 6d and 5d theories

Bhardwaj

Schäfer‐Nameki

2021

114

We describe general methods for determining higher-form symmetry groups of known 5d and 6d superconformal field theories (SCFTs), and 6d little string theories (LSTs). The 6d theories can be described as supersymmetric gauge theories in 6d which include both ordinary non-abelian 1-form gauge fields and also abelian 2-form gauge fields. Similarly, the 5d theories can also be often described as supersymmetric non-abelian gauge theories in 5d. Naively, the 1-form symmetry of these 6d and 5d theories is captured by those elements of the center of ordinary gauge group which leave the matter content of the gauge theory invariant. However, an interesting subtlety is presented by the fact that some massive BPS excitations, which includes the BPS instantons, are charged under the center of the gauge group, thus resulting in a further reduction of the 1-form symmetry. We use the geometric construction of these theories in M/F-theory to determine the charges of these BPS excitations under the center. We also provide an independent algorithm for the determination of 1-form symmetry for 5d theories that admit a generalized toric construction (i.e. a 5-brane web construction). The 2-form symmetry group of 6d theories, on the other hand, is captured by those elements of the center of the abelian 2-form gauge group that leave all the massive BPS string excitations invariant, which is much more straightforward to compute as it is encoded in the Green-Schwarz coupling associated to the 6d theory.

“…The defect group measures the defects which are not screened by dynamical objects, and as we will see, it is defined by the (relative) homology of W 6 . It has been shown that this object is readily computable through several methods [20][21][22][23][24][25][26][27][28][29][30][31] giving us considerable insight into the higher form symmetries of various field theories.…”

Section: Jhep10(2021)119mentioning

confidence: 99%

Maruyoshi-Song flows and defect groups of $$ {\mathrm{D}}_{\mathrm{p}}^{\mathrm{b}} $$(G) theories

Hosseini

Moscrop

2021

Self Cite

We study the defect groups of $$ {D}_p^b $$ D p b (G) theories using geometric engineering and BPS quivers. In the simple case when b = h∨(G), we use the BPS quivers of the theory to see that the defect group is compatible with a known Maruyoshi-Song flow. To extend to the case where b ≠ h∨(G), we use a similar Maruyoshi-Song flow to conjecture that the defect groups of $$ {D}_p^b $$ D p b (G) theories are given by those of G(b)[k] theories. In the cases of G = An, E6, E8 we cross check our result by calculating the BPS quivers of the G(b)[k] theories and looking at the cokernel of their intersection matrix.