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.