Abstract
We consider the circle and torus compactification of a certain subclass of 6d $\mathcal{N}=(1,0)$ SCFTs which are Higgsable to the higher rank E-string theories. Using the T-duality between Type I' and Type IIB, we found that the $S^1$ compactification of the theories can be realized by 5-brane webs describing the 5d uplifting of a specified class S theory, generalizing the result by Benini, Benvenuti and Tachikawa. We checked the above result by calculating conformal and flavor central charges of the 4d torus compactified theory both from the tensor branch structure of the 6d theory and from the predicted class S description.
Highlights
T-duality between Type I’ and Type IIB, we found that the S 1 compactification of the theories can be realized by 5-brane webs describing the 5d uplifting of a specified class S theory, generalizing the result by Benini, Benvenuti and Tachikawa
The leftmost tensor mode without gauge symmetry comes from the rank 1 E-string theory in figure 1 on its tensor branch
We find that the resulting 5-brane web configuration is that of figure 3, a three pronged junction of 5-branes terminated at 7branes
Summary
We describe the 6d theories T 6d {ui } of our interest from brane engineering in Type I’ [20, 21] (see [22,23,24]). We move the leftmost and the second leftmost D8 branes in the upper half of figure 2 on top of the O8− plane.4 In this process, the Hanany-Witten effect creates additional n7 = #{i =. We move other D8 branes near the NS5 stack to the region where x6 is very large and far away from all the NS5 branes. The Romans mass in the region where all the NS5 branes sit is again −6 and the number of D6 branes in the ith bunch is 6i + n7 + n8 + n9. The Ẽ1 theory has further mass deformation to the E0 theory which has no flavor symmetry This indicates that there are two distinct ways of splitting one D8 brane out of the stack of O8− plane and one D8 brane. The 5d SCFT from this web is the 5d b K {Y1 , Y2 , Y3 } of the class S theory TK {Y1 , Y2 , Y3 }
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