5d superconformal field theories and graphs

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

“…However, we choose a description that tracks the flavor symmetries Figure 2: This diagram shows schematically the approaches taken in the present paper and in the companion paper [31], where box graphs and Coulomb branch phases will be discussed. The CFDs were initially introduced in [8] and encode (among other things) the stronglycoupled flavor symmetry G (5d) F of the 5d SCFT. The present paper provides the geometric foundation for and a derivation of CFDs using the structure of "flavor curves" within compact surfaces in the resolution of Calabi-Yau threefold singularities.…”

Section: Part Ii: Box Graphs and Coulomb Branch Phasesmentioning

confidence: 99%

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

Apruzzi

Lawrie

Lin

et al. 2019

Self Cite

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.

“…As many of such 5d N = 1 theories can be engineered via Type IIB 5-brane webs [12,13] or M-theory on Calabi-Yau (CY) threefold [14,15], brane configurations also provide a direct description of the prepotential. For instance, one can study CY geometry of 5d gauge theories to obtain their triple intersections which yield the prepotential of the 5d theories or one can also scan possible gauge theory descriptions from the geometry which lead to a classification of the UV-dual theories [6,9,11,[16][17][18][19]. Though Type IIB 5branes can be understood as dual description of the geometry, not all CY geometries can be realized as a 5-brane web.…”

Section: Introductionmentioning

confidence: 99%

“…19) where we omitted constant terms which do not depend on the Coulomb branch moduli of the SU (3) gauge theories. Using the identity (2.11), we find that this agree with the IMS prepotential F…”

mentioning

confidence: 99%

Complete prepotential for 5d $$ \mathcal{N} $$ = 1 superconformal field theories

Hayashi

Kim

Lee

et al. 2020

For any 5d N = 1 superconformal field theory, we propose a "complete" prepotential which reduces to the perturbative prepotential for any of its possible gauge theory realizations, manifests its global symmetry when written in terms of the invariant Coulomb branch parameters, and is valid for the whole parameter region. As concrete examples, we consider SU (2) gauge theories with up to 7 flavors, Sp(2) gauge theories with up to 9 flavors, and Sp(2) gauge theories with 1 antisymmetric tensor and up to 7 flavors, as well as their dual gauge theories.