A Note on Superconformal N=2 theories and Orientifolds

TL;DR

Park and Uranga construct Type IIB orientifolds that are T-duals of elliptic Type IIA brane models with orientifold six-planes, yielding four-dimensional $\mathcal{N}=2$ finite theories. They show that twisted tadpole cancellation in the IIB setup is equivalent to the field-theory finiteness and classify two main families: (i) T-duals with O7 and D7 for the O$6^{-}$–O$6^{-}$ configuration, and (ii) orientifolds without D7s for the O$6^{+}$–O$6^{-}$ case, including both vector-structure and no-vector-structure branches. They provide explicit D3-brane Chan-Paton constructions at orientifold singularities that realize the spectra and derive tadpole conditions that reproduce the corresponding beta-function constraints. The work also connects these four-dimensional theories to six-dimensional RG fixed points and discusses potential AdS/CFT applications, highlighting new avenues to study $\mathcal{N}=2$ SCFTs via D3-branes at orientifold singularities.

Abstract

We construct the T duals of certain type IIA brane configurations with one compact dimension (elliptic models) which contain orientifold planes. These configurations realize four-dimensional $\NN=2$ finite field theories. For elliptic models with two negatively charged orientifold six-planes, the T duals are given by D3 branes at singularities in the presence of O7-planes and D7-branes. For elliptic models with two oppositely charged orientifold planes, the T duals are D3 branes at a different kind of orientifold singularities, which do not require D7 branes. We construct the adequate orientifold groups, and show that the cancellation of twisted tadpoles is equivalent to the finiteness of the corresponding field theory. One family of models contains orthogonal and symplectic gauge factors at the same time. These new orientifolds can also be used to define some six-dimensional RG fixed points which have been discussed from the type IIA brane configuration perspective.

Figures (2)

• Figure 1: The three families of brane configurations in the background of two negatively charged O6-planes. The short vertical lines represent the NS branes, the crossed circles are the orientifold planes, while uncircled crosses denote the D6 branes. The D4 branes stretch in the interval along the circle in $x^6$. In order to yield finite theories, the number of D4 branes is generically different at each interval. For the sake of clarity we have not attempted to draw them.
• Figure 2: The four families of theories arising in the O$6^{+}$-O$6^{-}$ configuration.