Strings of Minimal 6d SCFTs

TLDR: In this article, a quiver description for the n = 4 string using Sen's limit of F-theory and calculating its elliptic genus with localization techniques is presented. But the authors do not consider the topological string theory for other values of n.

Abstract: We study strings associated with minimal 6d SCFTs, which by defini- tion have only one string charge and no Higgs branch. These theories are labelled by a number n with 1 ≤ n ≤ 8 or n = 12. Quiver theories have previously been proposed which describe strings of SCFTs for n = 1,2. For n > 2 the strings interact with the bulk gauge symmetry. In this paper we find a quiver description for the n = 4 string using Sen's limit of F-theory and calculate its elliptic genus with localization techniques. This result is checked using the duality of F-theory with M-theory and topological string theory whose refined BPS partition function captures the elliptic genus of the SCFT strings. We use the topological string theory to gain insight into the elliptic genus for other values of n.

Figures

Figure 1: The quiver describing the O(−2) → P1 strings.

Figure 2: Configuration of (−2) curves that gives rise to the O(−2) → P1 local geometry. We have also indicated the degeneration of the elliptic fiber over each curve that gives rise to the M-string geometry.

Figure 7: Extended Dynkin diagram for D4.

Table 1: Table of Coxeter numbers Cg and Euler numbers χ(M3) for the different minimal SCFT Calabi-Yau threefolds.

Figure 3: The quiver for O(−1) → P1 strings.

Figure 6: Singular hyperplane configuration for the two-string elliptic genus. The vectors normal to the singular hyperplanes are displayed, along with the multiplicity with which they occur. Our choice of q is also displayed here.