Geometric constraints on the space of N=2 SCFTs. Part III: enhanced Coulomb branches and central charges

Abstract

This is the third in a series of three papers on the systematic analysis of rank 1 four dimensional N = 2 SCFTs. In the first two papers [1, 2] we developed and carried out a strategy for classifying and constructing physical planar rank-1 Coulomb branch geometries of N = 2 SCFTs. Here we describe general features of the Higgs and mixed branch geometries of the moduli space of these SCFTs, and use this, along with their Coulomb branch geometry, to compute their conformal and flavor central charges. We conclude with a summary of the state of the art for rank-1 N = 2 SCFTs.

Long multiplet bootstrap

“…16 Despite having no exactly marginal deformations, thus making them hard to study by the traditional field-theoretic approaches, various examples of non-trivial, pure, N = 3 SCFTs have been constructed by now [44,46,47] using string-theoretic technology. These theories were also recovered, and new ones obtained, by the systematic study of N = 2 SCFTs with a one complex dimensional Coulomb branch in the work of [48,49,91,92]. Nevertheless, we still seem far from having a complete classification of N = 3 SCFTs.…”

“…In a different direction, the blocks we have computed are precisely the ones relevant for the study of the chiral algebras associated to the recently discovered four-dimensional N = 3 SCFTs [44], further explored in [30,[44][45][46][47][48][49][50][51][52][53][54]. Here we take a purely field-theoretic approach to these theories, using the fact, shown in [55], that any four-dimensional theory with N 2 supersymmetry has a subsector isomorphic to a two-dimensional chiral algebra.…”

Geometric constraints on the space of N $$ \mathcal{N} $$ = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows

“…Column 2 lists the Kodaira type of the scale invariant CB geometry, column 3 the resulting singularity types under a generic relevant deformation, and column 4 the maximal flavor symmetry of the SCFT. The values for the central charges for the entries in the table are known and can be found in table 1 of [16].…”

“…The third paper [16] will focus on how to extract other N = 2 SCFT data, such as certain Higgs branch dimensions, and conformal and flavor central charges, from their CB geometries.…”

Dualities of deformed N = 2 $$ \mathcal{N}=2 $$ SCFTs from link monodromy on D3-brane states

“…gauge symmetry and seven-brane structures, which is central to certain phenomenological aspects of F-theory GUTs [18][19][20]; there is growing evidence that non-trivial seven-brane structures, so-called non-Higgsable clusters [21,22], are generic [22][23][24][25][26][27] in F-theory; and in recent years there has been a resurgence of interest in 6d (1,0) [28,29] and 4d N = 1 SCFTs [15,30] that arise from F-theory and in N = 2 SCFTs in general [31][32][33]. All of these typically involve strongly coupled physics.…”