(De)constructing Intersecting M5-branes

TL;DR

This work reframes intersecting M5-branes as a limit of a two-dimensional defect CFT with $(4,0)$ supersymmetry arising from intersecting D3-branes on a $\,\mathbb{C}^2/\mathbb{Z}_k$ orbifold. In the $k\rightarrow \infty$ limit, two extra dimensions emerge and the moduli map between the defect CFT and the M5-M5 system is established, linking the $(4,0)$ $SU(2)_L$ R-symmetry to the $SU(2)$ R-symmetry of the ${\cal N}=2$, $d=4$ intersection. The analysis identifies tensionless strings at the intersection as the quiver spokes, demonstrates an $\,SU(2)_L$ 't Hooft anomaly that would reflect in the four-dimensional theory, and elaborates how string condensation yields the holomorphic curve $xy=c$. Overall, the paper provides a concrete deconstruction-based framework for understanding M5-brane intersections and points to concrete future directions, including Chern-Simons contributions and extensions to more complex brane intersections.

Abstract

We describe intersecting M5-branes, as well as M5-branes wrapping the holomorphic curve xy=c, in terms of a limit of a defect conformal field theory with two-dimensional (4,0) supersymmetry. This dCFT describes the low-energy theory of intersecting D3-branes at a C^2/Z_k orbifold. In an appropriate k -> infinity limit, two compact spatial directions are generated. By identifying moduli of the M5-M5 intersection in terms of those of the dCFT, we argue that the SU(2)_L R-symmetry of the (4,0) defect CFT matches the SU(2) R-symmetry of the N =2, d=4 theory of the M5-M5 intersection. We find a 't Hooft anomaly in the SU(2)_L R-symmetry, suggesting that tensionless strings give rise to an anomaly in the SU(2) R-symmetry of intersecting M5-branes.

Figures (4)

• Figure 1: Quiver diagram for parallel D3-branes at a $\mathbb{C}^2/\mathbb{Z}_k$ orbifold (here $k=8$). Each node corresponds to an ${\cal N} =2$ vector multiplet, while double lines between neighboring nodes correspond to an $\mathcal{N}=2$ hypermultiplet.
• Figure 2: "Mating Moose": Quiver diagram for intersecting D3-branes at a $\mathbb{C}^2/\mathbb{Z}_k$ orbifold (with $k$=8). The nodes of the inner and outer circle are associated with the $SU(N')^k$ and $SU(N)^k$ gauge groups respectively. The parts which have not been drawn in the detailed "close-up" are easily inferred from the $\mathbb{Z}_k$ symmetry and by swapping D3 degrees of freedom with D$3^{\prime}$ degrees of freedom.
• Figure 3: (De)construction of two extra dimensions along the torus with radii $R$ and $R_D$. The common directions $x^0$ and $x^1$ as well as the four orbifold directions are surpressed.
• Figure 4: Strings localized at the intersection.