Quantum curves of 6d SCFTs on a -3 curve

Abstract

We study half-BPS defects and quantum Seiberg-Witten curves in 6d $\mathcal{N}=(1,0)$ SCFTs on a $-3$ curve. We compute the partition functions in the presence of codimension-4 and codimension-2 defects on ${\mathbb{R}}^4\times T^2$ using generalized blowup equations. We then propose quantum Seiberg-Witten curves as elliptic difference equations satisfied by the Nekrasov-Shatashvili limits of the defect partition functions. We apply this construction to the minimal $\mathfrak{su}(3)$ gauge theory, and to the ${\mathfrak{g}}_2$ and $\mathfrak{so}(N)$ gauge theories on a Higgsing tree whose endpoint is the minimal $\mathfrak{su}(3)$ theory. We also investigate defects and the quantum curve of the $\mathfrak{su}(3)$ gauge theory compactified on a circle with a ${\mathbb{Z}}_2$ twist.

arXiv comment42 pages