Classifying 5d SCFTs via 6d SCFTs: arbitrary rank

139

We consider compactifications of 6d minimal (D N +3 , D N +3 ) type conformal matter SCFTs on a generic Riemann surface. We derive the theories corresponding to three punctured spheres (trinions) with three maximal punctures, from which one can construct models corresponding to generic surfaces. The trinion models are simple quiver theories with N = 1 SU (2) gauge nodes. One of the three puncture non abelian symmetries is emergent in the IR. The derivation of the trinions proceeds by analyzing RG flows between conformal matter SCFTs with different values of N and relations between their subsequent reductions to 4d. In particular, using the flows we first derive trinions with two maximal and one minimal punctures, and then we argue that collections of N minimal punctures can be interpreted as a maximal one. This suggestion is checked by matching the properties of the 4d models such as 't Hooft anomalies, symmetries, and the structure of the conformal manifold to the expectations from 6d. We then use the understanding that collections of minimal punctures might be equivalent to maximal ones to construct trinions with three maximal punctures, and then 4d theories corresponding to arbitrary surfaces, for 6d models described by two M 5 branes probing a Z k singularity. This entails the introduction of a novel type of maximal puncture. Again, the suggestion is checked by matching anomalies, symmetries and the conformal manifold to expectations from six dimensions. These constructions thus give us a detailed understanding of compactifications of two sequences of six dimensional SCFTs to four dimensions. arXiv:1910.03603v1 [hep-th] 8 Oct 2019 7 Discussion 43 A N = 1 superconformal index 44 B Duality proof of symmetry enhancement 46 C Duality proof of exchanging minimal punctures 49

Section: Discussionmentioning

confidence: 99%

Sequences of 6d SCFTs on generic Riemann surfaces

Razamat

Sabag

2020

139

“…We will not consider the former as they give rise to "decoupled states" [74,92] that decouple in the SCFT limit, and moreover, the partition function including such states do not preserve the G F flavor symmetry [92]. The latter, which we refer to as (0)-curves give rise to the spin 1 BPS states of the SCFT.…”

Section: M2-branes Wrapping Genus Zero Curves With Normal Bundlementioning

confidence: 99%

Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states

Apruzzi

Lawrie

Lin

et al. 2019

164

278

We propose a graph-based approach to 5d superconformal field theories (SCFTs) based on their realization as M-theory compactifications on singular elliptic Calabi-Yau threefolds. Fieldtheoretically, these 5d SCFTs descend from 6d N = (1, 0) SCFTs by circle compactification and mass deformations. We derive a description of these theories in terms of graphs, so-called Combined Fiber Diagrams, which encode salient features of the partially resolved Calabi-Yau geometry, and provides a combinatorial way of characterizing all 5d SCFTs that descend from a given 6d theory. Remarkably, these graphs manifestly capture strongly coupled data of the 5d SCFTs, such as the superconformal flavor symmetry, BPS states, and mass deformations.The capabilities of this approach are demonstrated by deriving all rank one and rank two 5d SCFTs. The full potential, however, becomes apparent when applied to theories with higher rank. Starting with the higher rank conformal matter theories in 6d, we are led to the discovery of previously unknown flavor symmetry enhancements and new 5d SCFTs.

“…Another motivation to study these theories at present is recent progress in 6d SCFTs, where it is believed that a full classification of all UV-complete supersymmetric theories exists [4][5][6][7]. Indeed, recent works [1,2,[8][9][10][11][12][13][14] have suggested that all 5d N = 1 UVcomplete theories arise from appropriate circle reductions, possibly with holonomies for the global symmetries of 6d theories, thus conjecturing a classification of 5d theories.…”

Section: Introductionmentioning

confidence: 99%

Fibers add flavor. Part II. 5d SCFTs, gauge theories, and dualities

Apruzzi

Lawrie

Lin

et al. 2020

131

200

In [1, 2] we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d N = (1, 0) SCFTs. The graphs, so-called combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi-Yau threefold with a canonical singularity. In this paper we complement this geometric approach by connecting the CFD of an SCFT to its weakly coupled gauge theory or quiver descriptions and demonstrate that the CFD as recovered from the gauge theory approach is consistent with that as determined by geometry. To each quiver description we also associate a graph, and the embedding of this graph into the CFD that is associated to an SCFT provides a systematic way to enumerate all possible consistent weakly coupled gauge theory descriptions of this SCFT. Furthermore, different embeddings of gauge theory graphs into a fixed CFD can give rise to new UV-dualities for which we provide evidence through an analysis of the prepotential, and which, for some examples, we substantiate by constructing the M-theory geometry in which the dual quiver descriptions are manifest. arXiv:1909.09128v2 [hep-th]