Flopping and slicing: $\operatorname{SO}(4)$ and $\operatorname{Spin}(4)$-models

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.

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

164

278

“…As we are interested in gauge theories with an SCFT limit, we will focus either on theories where G gauge is a simple group that appears in in [40,44,50] and for specific low values of N in [49,51,54,[57][58][59][60][61], for Sp(N ) in [40,44,62], for SO(N ) in [40,44,63,64], and for the exceptional cases, G 2 , F 4 , E 6 , and E 7 in [63,65], [66], [44], and [44,67], respectively. In this paper we will not require an understanding of the full set of Coulomb phases, but, as we shall see momentarily, only of certain equivalence classes of the extended Coulomb phases for the theory after weakly gauging the classical flavor symmetry rotating the hypermultiplets, as it is these that can be related each to a distinct descendant gauge theory.…”

Section: Gauge Theory Phases and Box Graphs For Arbitrary Quiversmentioning

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]

“…This was done by explicitly performing resolutions of X T using methods described in detail in [9][10][11][12][13][14][15]. In this paper, we extend the work of [3] and provide a description of X T for T that are 6d SCFTs of any arbitrary rank (see [16][17][18] for related analyses of F-theory models involving collisions of elliptic fibers in cases of semi-simple, as opposed to simple, gauge algebras. ) We can use the data ofX T to perform RG flows to 5d SCFTs.…”

Section: Introductionmentioning

confidence: 99%

Classifying 5d SCFTs via 6d SCFTs: arbitrary rank

Bhardwaj

Jefferson

2019

111

175

According to a conjecture, all 5d SCFTs should be obtainable by rankpreserving RG flows of 6d SCFTs compactified on a circle possibly twisted by a background for the discrete global symmetries around the circle. For a 6d SCFT admitting an F-theory construction, its untwisted compactification admits a dual M-theory description in terms of a "parent" Calabi-Yau threefold which captures the Coulomb branch of the compactified 6d SCFT. The RG flows to 5d SCFTs can then be identified with a sequence of flop transitions and blowdowns of the parent Calabi-Yau leading to "descendant" Calabi-Yau threefolds which describe the Coulomb branches of the resulting 5d SCFTs. An explicit description of parent Calabi-Yaus is known for untwisted compactifications of rank one 6d SCFTs. In this paper, we provide a description of parent Calabi-Yaus for untwisted compactifications of arbitrary rank 6d SCFTs. Since 6d SCFTs of arbitrary rank can be viewed as being constructed out of rank one SCFTs, we accomplish the extension to arbitrary rank by identifying a prescription for gluing together Calabi-Yaus associated to rank one 6d SCFTs. 1 lbhardwaj@fas.harvard.edu 2 patrickjefferson@fas.harvard.edu 42 4.8 e 6 , e 7 , e 8 and f 4 48 4.9 su(3) on −3 50 -i -5 Gluing rules 50 5.1 Gluing of su(m), m ≥ 1 or m =6 and su(n), n ≥ 1 50 5.2 Gluing of sp(m), m ≥ 1 and su(n), n ≥ 1 52 5.3 Gluing of sp(m), m ≥ 1 and so(2r), r ≥ 4 52 5.4 Gluing of sp(m), m ≥ 1 and so(2r + 1), r ≥ 4 53 5.5 Gluing of sp(m), m ≥ 1 and so(7) 53 5.6 Gluing of sp(m), m ≥ 1 and g 2 54 5.7 Gluings of sp(0) = E-string 54 5.7.1 Simply laced 55 5.7.2 Non-simply laced 66 6 Future work 76 A User's guide for Mathematica notebook Pushforward.nb 77 • The set of compact holomorphic surfaces S i .