Abstract
Compactifications of 6d mathcal{N} = (1, 0) SCFTs give rise to new 4d mathcal{N} = 1 SCFTs and shed light on interesting dualities between such theories. In this paper we continue exploring this line of research by extending the class of compactified 6d theories to the D- type case. The simplest such 6d theory arises from D5 branes probing D-type singularities. Equivalently, this theory can be obtained from an F-theory compactification using −2- curves intersecting according to a D-type quiver. Our approach is two-fold. We start by compactifying the 6d SCFT on a Riemann surface and compute the central charges of the resulting 4d theory by integrating the 6d anomaly polynomial over the Riemann surface. As a second step, in order to find candidate 4d UV Lagrangians, there is an intermediate 5d theory that serves to construct 4d domain walls. These can be used as building blocks to obtain torus compactifications. In contrast to the A-type case, the vanishing of anomalies in the 4d theory turns out to be very restrictive and constraints the choices of gauge nodes and matter content severely. As a consequence, in this paper one has to resort to non- maximal boundary conditions for the 4d domain walls. However, the comparison to the 6d theory compactified on the Riemann surface becomes less tractable.
Highlights
6d SCFT such that the number of tensor multiplets is equal to the dimension of H1,1(B, Z)
It is found that the number of the Cartans of the global symmetry group is preserved along the RG flow from 6d to 4d and manifests itself as U(1) flavour symmetries of the 4d Lagrangian theory
By turning on fluxes for flavour symmetries, the SU(2k) flavour symmetry is broken to its Cartan subgroup U(1)2k−1 which mixes with the U(1)R-symmetry to give rise to a new R-symmetry in the IR
Summary
This section reviews the construction of the 6d model of D-type. Thereafter, the anomaly 8-form is derived and subsequently reduced along a Riemann surface. As shown in [13], the ON 0-plane results in a D-type quiver gauge theory on the tensor branch of the corresponding 6d N = (1, 0) theory. There exist (N + 1) tensor multiplets, one for each gauge group factor. One can determine the anomaly 8-form contributions from the vector and hypermultiplets encoded in the quiver (2.1) as well as the contributions of the (N +1) tensor multiplets. Summing all perturbative contributions of the N = (1, 0) multiplets, one finds the following pure gauge, mixed gauge R-symmetry, and mixed gauge flavour anomaly terms. ADN+1 denotes the Cartan matrix of DN+1, see [16, table VI], and the two (N + 1)-dimensional vectors ρ, γ are defined as follows:.
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