How geometric surgery in string theory reshapes quantum symmetries

String theorists flipping Calabi-Yau threefolds—geometric transitions that leave the physics intact—can now predict exactly how this surgery permutes the quantum charges carried by D-branes. The authors derive explicit formulas using a category-theoretic tool called the grade restriction rule, then verify the predictions against hemisphere partition functions from gauge theory. The result connects string geometry to knot invariants, offering a rare bridge between topological surgery and quantum field theory.