6d String Chains

TL;DR

This work develops a unified, computational framework for the self-dual strings arising on tensor branches of 6d (1,0) SCFTs realized in F-theory and related M-/Type II setups. By constructing explicit 2d (0,4) quiver gauge theories for bound states of strings in three classes—M5 branes probing ADE singularities, N small E8 instantons, and D5 branes probing ADE singularities—the authors compute elliptic genera via localization and confirm their results with 5d Sp(N) instanton calculus. A key outcome is the observation of factorization structures at m = ε+ in several setups, and the identification of anomaly-related refinements (or lack thereof) in D/E-type cases. The results provide a concrete computational dictionary linking 6d SCFT string dynamics to tractable 2d quiver descriptions and cross-checked instanton data, strengthening the utility of elliptic genera as probes of 6d physics.

Abstract

We consider bound states of strings which arise in 6d (1,0) SCFTs that are realized in F-theory in terms of linear chains of spheres with negative self-intersections 1,2, and 4. These include the strings associated to N small E8 instantons, as well as the ones associated to M5 branes probing A and D type singularities in M-theory or D5 branes probing ADE singularities in Type IIB string theory. We find that these bound states of strings admit (0,4) supersymmetric quiver descriptions and show how one can compute their elliptic genera.

Figures (15)

• Figure 1: Non-critical strings in M5 branes probing $A_{N-1}$ singularities.
• Figure 2: Convex chain of $-2$ curves.
• Figure 3: Type IIA brane setup corresponding to M5 branes probing $D_{p+4}$ a singularity. The fundamental strings depicted as blue or red wavy lines in this Figure give rise to fields in the 2d quiver theory.
• Figure 4: Non-critical strings in M5 branes probing $D_{p+4}$ singularities.
• Figure 5: E-strings as suspended M2 branes between M5 branes probing an M9 wall.