D2-brane probes of non-toric cDV threefolds via monopole superpotentials

[摘要] We develop a framework to construct worldvolume gauge theories on D2-branes probing compound Du Val (cDV) Calabi-Yau threefold singularities. By viewing these singularities as ADE surface fibrations over the complex w-plane, we encode their geometry in a Higgs field Φ(w). A D2-brane probe perceives Φ(w) as an 𝒩 = 2 deformation of its 3d 𝒩 = 4 affine Dynkin quiver gauge theory via polynomial and monopole superpotential terms. By exploiting 3d mirror symmetry, we obtain an effective theory that correctly reproduces the quiver-collapsing mechanism known in the mathematical literature. We present several examples, including non-toric and non-resolvable cases.

[发布日期] 2026-09-08

[关键词] D-Branes;Field Theories in Lower Dimensions;Supersymmetric Effective Theories;Differential and Algebraic Geometry