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

Abstract

This is the second in a series of three papers on systematic analysis of rank 1 Coulomb branch geometries of four dimensional N = 2 SCFTs. In [1] we developed a strategy for classifying physical rank-1 CB geometries of N = 2 SCFTs. Here we show how to carry out this strategy computationally to construct the Seiberg-Witten curves and one-forms for all the rank-1 SCFTs. Explicit expressions are given for all 28 cases, with the exception of the N f =4 su(2) gauge theory and the E n SCFTs which were constructed in [2,3] and [4,5].

Compactifications of 5d SCFTs with a twist

“…There is indeed a rank 1 isolated SCFT with USp(10) global symmetry, first found in [29]. Furthermore this SCFT indeed has a mass deformation leading to the SU(2) × USp(6) SCFT [30]. We can also compute the Higgs branch dimension finding d H = 16 which agrees with the known Higgs branch dimension of the USp(10) SCFT [30].…”

“…Again the previous discussion leads use to conclude that the resulting 4d theory is SO(3) + 3V which is again IR free. Such a mass deformation of the SU(2) × USp(6) SCFT was also found in [30]. Figure 7.…”

“…This is especially true for the theories introduced in section 3.2 particularly the rank 1 F 4 theory. Recently a systematic study of rank 1 N = 2 SCFTs was initiated in [21,30,42], and it is interesting if this can support or disfavor its existence. Furthermore the existence of a rank 1 F 4 SCFT was suspected from the superconformal bootstrap analysis in [43,44], which also calculated some of its central charges.…”

“…Therefore the 4d SU(2) × USp(6) SCFT, resulting from the Z 2 twisted compactification of the 5d SCFT in figure 3, should have a mass deformation leading to the 4d gauge theory SU(2) + 1S + 2F . Recently the mass deformations of the SU(2) × USp(6) SCFT were analyzed using the Seiberg-Witten curve in [30] who found that it indeed possess such a mass deformation.…”

“…It has an SU(4) × U(1) 2 global symmetry so we expect the 4d theory to have USp(4)×U(1) global symmetry. There is indeed a mass deformation of the SU(2) × USp(6) SCFT with that pattern of symmetry breaking leading to an isolated 4d SCFT with USp(4) × U(1) global symmetry [30]. It is natural to identify the resulting 4d SCFT with this theory.…”