Brane webs in the presence of an $O5^-$-plane and 4d class S theories of type D

TL;DR

This work proposes that 5d SCFTs engineered by brane webs in the presence of an $O5^-$-plane, when compactified on a circle, give rise to 4d class S theories of type $D$ derived from the $D_N(2,0)$ theory on a punctured sphere. The authors develop a dictionary linking 5d web data (global symmetries, Higgs-branch structure) to 4d $D$-type class S data, and test it by comparing central charges and operator spectra for dual realizations that should describe the same 4d theory. They present evidence that different 5d string constructions yielding the same 5d SCFT lead to identical 4d class S theories, and they extend the analysis to theories with marginal deformations (more punctures) as well as to isolated vs. marginal cases. The findings provide a geometric lift and cross-dimension consistency check that also hints at 3d dualities and prompts further exploration of the full lifts of certain $D_N$ theories and other orientifold-based webs.

Abstract

In this article we conjecture a relationship between 5d SCFT's, that can be engineered by 5-brane webs in the presence of an $O5^-$-plane, and 4d class S theories of type D. The specific relation is that compactification on a circle of the former leads to the latter. We present evidence for this conjecture. One piece of evidence, which is also an interesting application of this, is that it suggests identifications between different class S theories. This can in turn be tested by comparing their central charges.

Figures (18)

• Figure 1: An example for the Higgs branch of a $5d$ SCFT of the form considered in this article. The total Higgs branch dimension in this example is $8$, which we separate to four contributions which in this case happen to be equal. First we can pairwise break and separate the D$5$-branes along the D$7$-branes on one side of the orientifold. In this case there are two such directions for each side of the $O5$-plane, where there is an arrow representing the pair. There are also two directions given by pairwise breaking and separating the four D$5$-branes stretching between the two groups of D$7$-branes on either side of the $O5$-plane. Finally we can pairwise break and separate the NS$5$-branes along the $(0,1)$$7$-branes. In this case there are two directions, one given by breaking the longer part of the right NS$5$-branes while the other by separating the remaining part of the NS$5$-branes from the $O5$-plane.
• Figure 2: The mapping between the allocation of D$5$-branes on the $(1,0)$$7$-branes and the associated puncture. In all cases the $6d$ theory is the $(2,0)$ theory of type $D_{N}$ where $N$ is determined as explained in the text.
• Figure 3: The mapping between the allocation of NS$5$-branes on the $(0,1)$$7$-branes and the associated puncture. In all cases the $6d$ theory is the $(2,0)$ theory of type $D_{N}$ where $N$ is determined as explained in the text.
• Figure 4: Constructing the $5d$ gauge theories $USp(2N)+(2N+4)F$ (a) and $USp(2N)+(2N+5)F$ (b) using an $O5$-plane. The upper part shows the webs describing the $5d$ SCFT's. These webs are of the form we consider and so we conjecture that their compactification on a circle results in the $D$ type class S theories shown below them.
• Figure 5: Constructing the $5d$ gauge theories $USp(2N)+(2N+4)F$ (a) and $USp(2N)+(2N+5)F$ (b) using a resolved $O7^-$-plane. The left part shows the webs one gets after resolving the $O7^-$-plane. By performing a series of $7$-brane motions these can be recast into the the form of BB. The resulting webs are shown in the middle part of the figure. Upon compactification to $4d$, these are expected to give the type $A$ class S theories shown on the right.