Hanany-Witten effect and SL(2,Z) dualities in matrix models

Understand

We provide tests of dualities for three-dimensional N=4 quiver SCFTs with brane realizations in IIB string theory, by matching their exact partition functions on $S^3$.

• The dualities are generated by SL(2,Z) transformations and Hanany-Witten 5-brane moves.
• These contain mirror symmetry as well as dualities identifiying fixed points of Yang-Mills quivers and Chern-Simons theories.
• The partition function is given by a matrix model, that can be nicely rearranged into a sequence of factors mimicking the brane realization.