Thermodynamic limit for SO(2N) gauge theories with spinors/conjugate spinors

Abstract

In this paper, we investigate five-dimensional $\mathcal{N} = 1$ supersymmetric $SO(2N)$ gauge theories coupled to hypermultiplets in spinor/conjugate spinor representation based on 5-brane web constructions with O5-planes. Based on the topological vertex formalism with O5-plane, we find new expressions for the partition functions for these theories, emphasizing the difference between the case with two spinors and that with one spinor and one conjugate spinor. Through the thermodynamic limit of these partition functions, we derive the Cameral and Seiberg-Witten curves. We show that the difference between the spinor and the conjugate spinor appears as a difference in the boundary conditions of the Seiberg-Witten curves at the orientifold planes.