Backreacting D-brane instantons on branes at singularities

Non-perturbative D-brane instanton effects in 4d N = 1 string compactifications can be geometrized in terms of a backreacted generalized geometry. We extend earlier results to setups in which the D-brane instanton is charged under the 4d gauge symmetries, and show that the backreacted topology yields the correct charged field theory operators in the 4d effective action. In type IIA models with D6-branes, the backreaction of D2-brane instantons forces the recombination of D6-branes, such that the 4d charged field theory operators arise from basic worldsheet instantons in the backreacted geometry. We provide large classes of examples of D2-brane instanton effects on intersecting D6-brane systems in local models mirror to D3-branes at singularities. The backreacted geometry and the field theory operators are easily encoded in terms of simple operation in the graphs arising from the underlying dimer diagrams. This description agrees, in the appropriate cases, with the complex deformations triggered by certain fractional branes at the bottom of duality cascades.