On orbifolds of M-Strings

TL;DR

This work analyzes M-theory with $M$ parallel M5-branes probing a transverse $A_{N-1}$ singularity, establishing a 6d $(1,0)$ SCFT whose supersymmetric partition function on $T^2$ is computed via refined topological strings and the topological vertex, equivalently as the elliptic genus of a $\\\\mathbb{Z}_N$ orbifold of M-strings. The authors demonstrate that the resulting 2d theory on the M_A-strings is a $(4,0)$ quiver whose Higgs branch matches the moduli space of $SU(N)^{M-1}$ instantons on $\\mathbb{R}^4$, with right-moving fermions coupled to a specific bundle, and show how the partition function can be assembled from domain-wall amplitudes into a closed form $Z_M^{A_{N-1}}$ expressed in terms of Jacobi theta functions with a holomorphic anomaly. The paper develops multiple dual descriptions (Type IIB brane webs, 5d/6d gauge theories, and toric Calabi–Yau geometries) and provides a direct computation of the MA-string elliptic genus Ell$(N,\\vec{k})$, linking 6d indices to elliptic genera of 2d quiver theories. These results offer a concrete computational framework for 6d $(1,0)$ theories and their orbifold descendants, with potential extensions to D/E-type singularities and connections to 5d/4d reductions and Omega-backgrounds.

Abstract

We consider M-theory in the presence of M parallel M5-branes probing a transverse A_{N-1} singularity. This leads to a superconformal theory with (1,0) supersymmetry in six dimensions. We compute the supersymmetric partition function of this theory on a two-torus, with arbitrary supersymmetry preserving twists, using the topological vertex formalism. Alternatively, we show that this can also be obtained by computing the elliptic genus of an orbifold of recently studied M-strings. The resulting 2d theory is a (4,0) supersymmetric quiver gauge theory whose Higgs branch corresponds to strings propagating on the moduli space of SU(N)^{M-1} instantons on R^4 where the right-moving fermions are coupled to a particular bundle.

Figures (14)

• Figure 1: Compactification of the M5-brane theory on a circle in the presence of an $A_{n-1}$ singularity leads to the 5d quiver gauge theory depicted here.
• Figure 2: Type IIB brane web.
• Figure 3: Type IIB brane web with mass deformation.
• Figure 4: Dual six-dimensional quiver gauge theory.
• Figure 5: M-strings versus M$_{A}$-strings. In (a) the gauge group is $U(1)$ and the corresponding instantons originating from stretched M2-branes have zero size in the $\mathbb{R}^4_\parallel$ directions. In (b) we see a thickening of the M2-brane ending on the M5-brane in the case of transverse $A_{N-1}$ singularity, because instantons can now acquire a finite size.