Holography for (1,0) theories in six dimensions

Abstract

M-theory and string theory predict the existence of many six-dimensional SCFTs. In particular, type IIA brane constructions involving NS5-, D6-and D8-branes conjecturally give rise to a very large class of N = (1, 0) CFTs in six dimensions. We point out that these theories sit at the end of RG flows which start from six-dimensional theories which admit an M-theory construction as a M5 stack transverse to R 4 /Z k × R. The flows are triggered by Higgs branch expectation values and correspond to D6's opening up into transverse D8-branes via a Nahm pole. We find a precise correspondence between these CFT's and the AdS 7 vacua found in a recent classification in type II theories. Such vacua involve massive IIA regions, and the internal manifold is topologically S 3 . They are characterized by fluxes for the NS three-form and RR two-form, which can be thought of as the near-horizon version of the NS5's and D6's in the brane picture; the D8's, on the other hand, are still present in the AdS 7 solution, in the form of an arbitrary number of concentric shells wrapping round S 2 's.

Holographic flows in non-Abelian T-dual geometries

“…Our result for the central charge c ∼ N 2 D6 N 3 N S5 suggest that we are dealing with QFT similar to those recently studied in [63,80]. It would be important to make this correspondence sharper.…”

“…(3.19) above is, up to a normalisation factor, the one obtained in equation (5.5) of the work by Gaiotto and Tomasiello [63]. In their case, the physical system is composed by k = N D6 D6 branes, D8 branes and N = (n + 1)-NS five branes.…”

Geometric engineering, mirror symmetry and 6 d 1 0 → 4 d N = 2 $$ 6{\mathrm{d}}_{\left(1,0\right)}\to 4{\mathrm{d}}_{\left(\mathcal{N}=2\right)} $$

“…Note that this reduction preserves the SU(N ) × SU(N ) flavor symmetry of the 6d theory. This setup should generalize to all models of [22] which correspond to adding Nahm pole boundary conditions in a massive type IIA setup or, equivalently, Tbranes in an F theory engineering [23]. These models in 6d correspond to a linear quiver with decorations on the sides characterized in terms of embeddings of µ L , µ R : su 2 → G, encoding the flavor symmetry.…”

Elliptic genus of E-strings

“…They are rather enigmatic as they include tensionless self-dual strings as their building blocks. The study of these theories has recently intensified, leading to computations of their superconformal indices [1][2][3][4], the elliptic genera of the self-dual strings in the Coulomb branch [5][6][7] (see [8] for an earlier work), as well as a partial classification of 6d superconformal theories [9][10][11]. The aim of this paper is to take a step forward in this direction, in particular focusing on one of the most basic (1, 0) superconformal theories.…”