Superconformal fixed points with En global symmetry

Abstract

We obtain the elliptic curve and the Seiberg-Witten differential for an N = 2 superconformal field theory which has an E 8 global symmetry at the strong coupling point τ = e πi/3 .The differential has 120 poles corresponding to half the charged states in the fundamental representation of E 8 , with the other half living on the other sheet. Using this theory, we flow down to E 7 , E 6 and D 4 . A new feature is a λ SW for these theories based on their adjoint representations. We argue that these theories have different physics than those with λ SW built from the fundamental representations.10/96

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

“…or so(7) flavor symmetry 55 A.1.5 {I 3 , I * 1 }, {I 1 2 , I * 2 }, and {I 1 , I * 3 } 56 A.1.6 {I 1 2 , IV * } with G 2 flavor symmetry 57 A.1.7 {I 2 , IV * } with su(2) flavor symmetry 58 A.1.8 {I 1 , III * } with su(2) flavor symmetry 59 A.2 Deformations of the III * singularity 60 A.2.1 {I 5 1 , I 4 } with sp(6) ⊕ su(2) flavor symmetry 60…”

“…Section 4 describes how to construct the SW one-form. Our method is a slight generalization of one introduced by Minahan and Nemeschansky [4,5]. The existence of the SW one-form generally involves finding solutions of an over-constrained system of equations.…”

“…The SL(2, Z) group of electric-magnetic (EM) duality transformations acts linearly on charge vectors. It is useful to specify a particular set of generators of SL(2, Z), 5) which satisfy the relations S 2 = (ST ) 3 = −I. There are two basic EM-duality invariants built from the charges.…”

“…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]. …”

A holographic computation of the central charges ofd= 4, 𝒩 = 2 SCFTs

“…The superconformal R-symmetry is an accidental symmetry at the infrared fixed point, so we do not have any effective means of calculating the 't Hooft anomalies in the language of the four dimensional field theory. For the 7-brane of type E n , the corresponding SCFTs on a single D3-brane were first discussed in [9,10] and were studied shortly thereafter in detail by [11,12]. A purely field-theoretical construction of these theories was not known until quite recently when the paper [15] appeared, which motivated us to re-analyze these theories.…”