(5d RG-flow) trees in the tropical rain forest

Abstract

5d superconformal field theories (SCFTs) can be obtained from 6d SCFTs by circle compactification and mass deformation. Successive decoupling of hypermultiplet matter and RG-flow generates a decoupling tree of descendant 5d SCFTs. In this paper we determine the magnetic quivers and Hasse diagrams, that encode the Higgs branches of 5d SCFTs, for entire decoupling trees. Central to this undertaking is the approach in [1], which, starting from the generalized toric polygons (GTPs) dual to 5-brane webs/tropical curves, provides a systematic and succinct derivation of magnetic quivers and their Hasse diagrams. The decoupling in the GTP description is straightforward, and generalizes the standard flop transitions of curves in toric polygons. We apply this approach to a large class of 5d KK-theories, and compute the Higgs branches for their descendants. In particular we determine the decoupling tree for all rank 2 5d SCFTs. For each tree, we also identify the flavor symmetry algebras from the magnetic quivers, including non-simply-laced flavor symmetries.

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

“…This matches the rank computed from the GTP using the generalised s-rule [30,35]. 15 For instance, for the partitions of N = 5 appearing in (5.7), we have:…”

“…Moreover, the 3d theories EQ (4) and MQ (5) , in that case, can be described by 3d quiver gauge theories with (special) unitary gauge groups. We can then fruitfully compare our results to complementary approaches that use magnetic quivers derived from brane webs [41,42,[45][46][47][48][49][50][51][52] or from the dual generalized toric polygons [30,35]. Note that our setup implicitly assumes that we obtain a well-defined 4d SCFT in the IR of D S 1 T 5d X , at the origin of the 4d CB; in particular, we assume the 5d Higgs branch consists of a single cone.…”

“…These branes webs can be efficiently represented as dot diagrams [63], also known as a generalized toric polygons (GTP) [30,35]. In particular, given a GTP, there is a systematic algorithm (either based on brane-web technology [46,97] or directly in the GTP [30]) for computing the magnetic quiver of the SCFT defined by the brane web/GTP, whenever that magnetic quiver is 'good' or 'ugly' [30,35]. In the present setup, all GTP are triangles related to the T N theory.…”

Factorised 3d $$ \mathcal{N} $$ = 4 orthosymplectic quivers

“…recent development is to use 3d N = 4 theories as a probe to study higher dimensional superconformal field theories (SCFTs) as well as gauge theories [2][3][4][5][6][7][8][9][10][11][12][13][14]. The idea is to relate the Higgs branch of these higher dimensional theories to the Coulomb branch of the 3d theory, the latter of which is dubbed magnetic quiver (MQ).…”

“…The first subdivision was already discussed in [2], while the second and third were overlooked. It was noticed in [9] that there should be 2 additional OSp cones to match the analysis on the unitary side. We claim that the missing cones in this case correspond to the two new maximal subdivisions appearing in figure 5.…”