Mutation, Witten Index, and Quiver Invariant

Understand

We explore Seiberg-like dualities, or mutations, for ${\cal N}=4$ quiver quantum mechanics in the context of wall-crossing.

• In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care.
• With fixed Fayet-Iliopoulos constants, at most two nodes can be mutated, one left and the other right, mapping a chamber of a quiver into a chamber of a mutated quiver.
• We delineate this complex pattern for triangle quivers and show how the Witten indices are preserved under such finely chosen mutations.