Seiberg-Witten geometry of four-dimensional N=2 SO-USp quiver gauge theories, I

Abstract

We apply the instanton counting method to study a class of four-dimensional $\mathcal{N}=2$ supersymmetric quiver gauge theories with alternating $\mathrm{SO}$ and $\mathrm{USp}$ gauge groups. We compute the partition function in the $\Omega$-background and express it as functional integrals over density functions. Applying the saddle point method, we derive the limit shape equations which determine the dominant instanton configurations in the flat space limit. The solution to the limit shape equations gives the Seiberg-Witten geometry of the low energy effective theory. As an illustrating example, we work out explicitly the Seiberg-Witten geometry for linear quiver gauge theories. Our result matches the Seiberg-Witten solution obtained previously using the method of brane constructions in string theory.

30 pages; v4: minor typos corrected, published version

References in corpus (4)

• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• Instanton counting with a surface operator and the chain-saw quiver
• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• N=2 S-duality via Outer-automorphism Twists

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• Orthosymplectic Superinstanton Counting and Brane Dynamics
• $\mathcal{N}=1$ Curves on Generalized Coulomb Branches
• A note on chiral trace relations from qq-characters