Elliptic quantum curves of 6d SO(N) theories

Abstract

Abstract We discuss supersymmetric defects in 6d $$ \mathcal{N} $$ N = (1, 0) SCFTs with SO(Nc) gauge group and Nc− 8 fundamental flavors. The codimension 2 and 4 defects are engineered by coupling the 6d gauge fields to charged free fields in four and two dimensions, respectively. We find that the partition function in the presence of the codimension 2 defect on ℝ4× 𝕋2 in the Nekrasov-Shatashvili limit satisfies an elliptic difference equation which quantizes the Seiberg-Witten curve of the 6d theory. The expectation value of the codimension 4 defect appearing in the difference equation is an even (under reflection) degree Nc section over the elliptic curve when Nc is even, and an odd section when Nc is odd. We also find that RG-flows of the defects and the associated difference equations in the 6d SO(2N + 1) gauge theories triggered by Higgs VEVs of KK-momentum states provide quantum Seiberg-Witten curves for ℤ2 twisted compactifications of the 6d SO(2N) gauge theories.