1/4 BPS String Junctions and $N^3$ Problem in 6-dim (2,0) Superconformal Theories

TL;DR

The paper addresses how the $N^3$ scaling of degrees of freedom in 6d $(2,0)$ ADE theories emerges by identifying 1/4 BPS objects in the Coulomb phase as waves on selfdual strings and three-string junctions. By leveraging 5d monitorings of BPS states and anomaly considerations, the authors show that the total number of 1/4 BPS objects (and anti-objects) across ADE types equals $\frac{1}{3} c_G$ with $c_G = d_G h_G$, matching the anomaly coefficient. This exact matching across $A$, $D$, and $E$ types provides evidence that these BPS structures encode the sought-after $N^3$ degrees of freedom in the Coulomb phase and could contribute to the low-energy dynamics. The results further imply a nuanced structure for E-type theories where the count does not simply correspond to a representation dimension, motivating deeper connections to anomaly arguments and nonperturbative M5-brane physics.

Abstract

We explore 1/4 BPS objects in the Coulomb phase of the ADE-type 6-dim (2,0) superconformal theories. By using the previous work on the junctions of strings in 5-dim gauge theories and 6-dim superconformal theories, we count the number of 1/4 BPS objects, which are made of waves on selfdual strings and junctions of selfdual strings and show that for all cases the number matches exactly one third of the anomaly constant $c_G=d_G h_G$ which is the product of dimension $d_G$ and dual Coxeter number $h_G$. This suggests the long sought after $N^3$ degrees of freedom are these 1/4 BPS objects at least in the Coulomb phase.

Figures (8)

• Figure 1: two representations of 1/4 left and right moving BPS waves on a selfdual string
• Figure 2: Triangle and 1/4 BPS Junction and Anti-Junction
• Figure 3: Energy scale in the Coulomb phase
• Figure 4: A-type Junction and Anti-Junction
• Figure 5: D-type Junctions and Anti-Junctions