Elliptic Quantum Curves of 6d SO(N) theories

Abstract

We discuss supersymmetric defects in 6d $\mathcal{N}=(1,0)$ SCFTs with $\mathrm{SO}(N_c)$ gauge group and $N_c-8$ 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 ${\mathbb{R}}^4\times {\mathbb{T}}^2$ 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 $N_c$ section over the elliptic curve when $N_c$ is even, and an odd section when $N_c$ is odd. We also find that RG-flows of the defects and the associated difference equations in the 6d $\mathrm{SO}(2N+1)$ gauge theories triggered by Higgs VEVs of KK-momentum states provide quantum Seiberg-Witten curves for ${\mathbb{Z}}_2$ twisted compactifications of the 6d $\mathrm{SO}(2N)$ gauge theories.

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Cited by in corpus (6)

• Topological strings and Wilson loops
• ABCD of qq-characters
• Seiberg-Witten curves with O7${}^{\pm }$-planes
• $C_2$ generalization of the van Diejen model from the minimal $(D_5,D_5)$ conformal matter
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants