Higgsing towards E-strings

TL;DR

The paper develops anomaly-free 2d $(0,4)$ gauge theories that describe self-dual strings in 6d $(1,0)$ SCFTs along Higgsing cascades toward the E-string. By computing elliptic genera and employing FI deformations, it uncovers IR symmetry enhancements (e.g., SU(12) for SU(3) with 12 flavors, SO(20)/SU(10)×U(1) for SU(2) with 10 flavors, and E8 for E-strings) and provides UV completions for the associated instanton moduli spaces. It extends the framework to multiple M5-branes probing an M9-wall, yielding refined spectra and quivers that realize full E8 symmetry in the tensor branch and align with 5d Sp(n) instanton calculus. The results offer a robust bridge between 2d worldsheet theories, 6d SCFT dynamics, and their lower-dimensional dual descriptions. This advances understanding of UV completions for instanton strings and the realization of flavor symmetries in high-dimensional theories via 2d gauge theories and their indices.

Abstract

We explore 6d (1,0) superconformal field theories with SU(3) and SU(2) gauge symmetries which cascade after Higgsing to the E-string theory on a single M5 near an $E_8$ wall. Specifically, we study the 2d $\mathcal{N}=(0,4)$ gauge theories which describe self-dual strings of these 6d theories. The self-dual strings can be also viewed as instanton string solitons of 6d Yang-Mills theories. We find the 2d anomaly-free gauge theories for self-dual strings, amending the naive ADHM gauge theories which are anomalous, and calculate their elliptic genera. While these 2d theories respect the flavor symmetry of each 6d SCFT only partially, their elliptic genera manifest the symmetry fully as these functions as BPS index are invariant in strongly coupled IR limit. Our consistent 2d (0,4) gauge theories also provide new insights on the non-linear sigma models for the instanton strings, providing novel UV completions of the small instanton singularities. Finally, we construct new 2d quiver gauge theories for the self-dual strings in 6d E-string theory for multiple M5-branes probing the $E_8$ wall, and find their fully refined elliptic genera.

Figures (7)

• Figure 1: IIA brane system for 6d $SU(N)$ theory Higgsable to M-string theory
• Figure 2: UV gauge theory on $SU(N)$ self-dual strings in the M-string Higgsing chain
• Figure 3: IIA brane system for 6d $SU(N)$ theory Higgsable to E-string theory
• Figure 4: UV gauge theory on $SU(N)$ self-dual strings in the E-string Higgsing chain
• Figure 5: UV gauge theory obtained via the FI deformation of Figure \ref{['fig:2d-quiver']}