Seiberg Duality, 5d SCFTs and Nekrasov Partition Functions

Abstract: It is known that a 4d N = 1 SCFT lives on D3-branes probing a local del Pezzo Calabi-Yau singularity. The Seiberg (or toric) duality of this SCFT arises from the Picard-Lefshetz transformation of the affine E_N 7-brane background that is associated with the Calabi-Yau threefold. In this paper we study the duality of the affine E_N background itself and a 5-brane probing it. We then find that many different Type IIB 5-brane webs describe the same SCFT in 5d. We check this duality by comparing the Nekrasov partition functions of these 5-brane web configurations.