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

Abstract

We use the AdS/CFT correspondence to compute the central charges of the d = 4, N = 2 superconformal field theories arising from N D3-branes at singularities in F-theory. These include the conformal theories with E n global symmetries. We compute the central charges a and c related to the conformal anomaly, and also the central charges k associated to the global symmetry in these theories. All of these are related to the coefficients of ChernSimons terms in the dual string theory on AdS 5 . Our computation is exact for all values of N , enabling several tests of the dualities recently proposed by Argyres and Seiberg for the E 6 and E 7 theories with N = 1.

BPS states in the Minahan-Nemeschansky $${E_6}$$ theory

“…This gives a check of our formalism. 4. We show that BPS states exist with all primitive charges, i.e.…”

“…for a few highlights see [2,3,4,5,6].) In [7], it was shown that T 3 can be constructed as a theory of class S[A 2 ] (see [8] for more on the definition of class S).…”

6d N = 1 0 $$ \mathcal{N}=\left(1,0\right) $$ theories on T2 and class S theories. Part I

“…When put on T 2 , this is known to reduce to the general-rank version of the E 8 theory of Minahan and Nemeschansky. The central charges a, c and k of these theories were found in [31]:…”

The BPS spectrum of the 4d $ \mathcal{N}=2 $ SCFT’s H 1, H 2, D 4, E 6, E 7, E 8

“…a D 2 (G) theory [12] (for D 4 AD these two chambers are equivalent). where ∆ is the dimension of the field parametrizing the Coulomb branch of the rank 1 SCFT, and n 7 is the number of parallel 7-branes needed to engineer the SCFT in F -theory [1][2][3][4][5][6][7][8][9]; see Table 1.…”

“…Consider the seven rank 1 4d N = 2 SCFT's which may be engineered in F -theory using the Kodaira singular fibers [1][2][3][4][5][6][7][8][9] H 0 , H 1 , H 2 , D 4 , E 6 , E 7 , E 8 .…”