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 E8 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 E8 wall, and find their fully refined elliptic genera.
Highlights
Apart from the minimal SU(3) case with Nf = 0, the above theories are obtained by enhancing M-string and E-string theories with gauge symmetries and extra matters
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 E8 wall
Looking at the BPS spectrum after q-expansion, we find that the elliptic genera exhibit the global symmetry enhancement from SU(11)×U(1)F to SU(12)
Summary
We construct the anomaly-free (0, 4) gauge theories for k self-dual strings in the following sequences of 6d gauge theories:. It is because only the first one realizes the SO(4) global symmetry of M-string theory, which rotates 4 transverse directions to M5-branes Let us decompose it into SO(4) = SU(2)L × SU(2)R. As a 6d fundamental hypermultiplet induces a (0, 4) Fermi multiplet in the 2d ADHM construction, one may naively attempt to describe k self-dual strings by adding 6 more Fermi multiplets to figure 2 This trial immediately fails because a gauge anomaly vanishes only if Nf = 2N. Recall that inclusion of a 5d SU(2) antisymmetric hypermultiplet, which decoupled in the perturbative gauge theory, was crucial for the correct UV completion of instanton quantum mechanics [60] of the D0-D4-D8-O8 brane systems This class (N, Na, Nf ) = (N, 1, N + 8) of 6d SCFTs can be realized as the IIA brane system [9]. This compact branch resolves the degrees of freedom localized at the small instanton singularity, intersecting with the usual instanton moduli space for nonzero q and q
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