Duality cascades and affine Weyl groups

A bstract Brane configurations in a circle allow subsequent applications of the Hanany-Witten transitions, which are known as duality cascades. By studying process cascades corresponding to quantum curves with symmetries Weyl groups, we find hidden structure affine groups. Namely, fundamental domain consisting all final destinations is characterized by chamber and realized translations group, where overall rank brane configuration associates grading operator algebra. The group guarantees finiteness processes uniqueness endpoint In addition original cascades, can generalize cases Fayet-Iliopoulos parameters. There utilize analyze similarly that continues be chamber. We further interpret impose “half” transition.