We start considering the problem of a D3 brane ending on pqwebs of 5 branes. We find the N=2 3d theories describing the systems and show that they admit different dual descriptions, related by 'piece-wise' Abelian mirror symmetry. Interestingly, some of the dual phases involve monopole operators in the superpotential. In the simplest case, U(1) with 3 flavors and monopole superpotential has a dual description as a cubic Wess-Zumino model. When projected to the S^3 partition function, this duality gives a physical explanation of an integral identity known as 'new pentagon' or 'ultimate integral'. We also consider generalizations to non Abelian gauge theories, leading to Aharony-Seiberg dualities with monopole superpotentials.
Based on http://arxiv.org/pdf/1605.02675.pdf , S.B. and Sara Pasquetti.
