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Superconformal field theories from M-theory crystal lattices

2007; American Physical Society; Volume: 75; Issue: 10 Linguagem: Inglês

10.1103/physrevd.75.101901

1550-7998

Sangmin Lee,

Particle physics theoretical and experimental studies

We propose a brane configuration for the $(2+1)\mathrm{d}$, $\mathcal{N}=2$ superconformal theories (${\mathrm{CFT}}_{3}$) arising from M2 branes probing toric Calabi-Yau 4-fold cones, using a T-duality transformation of M theory. We obtain intersections of M5-branes on a three-torus which form a 3d bipartite crystal lattice in a way similar to the 2d dimer models for ${\mathrm{CFT}}_{4}$. The fundamental fields of the ${\mathrm{CFT}}_{3}$ are M2-brane discs localized around the intersections, and the superpotential terms are identified with the atoms of the crystal. The model correctly reproduces the Bogomol'nyi-Prasad-Sommerfield (BPS) spectrum of mesons.