Aspects of 5d Seiberg-Witten Theories on ${\mathbb{S}}^1$

Abstract

We study the infrared physics of 5d $\mathcal{N}=1$ Yang-Mills theories compactified on ${\mathbb{S}}^1$, with a view toward 4d and 5d limits. Global structures of the simplest Coulombic moduli spaces are outlined, with an emphasis on how multiple planar 4d Seiberg-Witten geometries are embedded in the cigar geometry of a single 5d theory on ${\mathbb{S}}^1$. The Coulomb phase boundaries in the decompactification limit are given particular attention and related to how the wall-crossings by 5d BPS particles turn off. On the other hand, the elliptic genera of magnetic BPS strings do wall-cross and retain the memory of 4d wall-crossings, which we review with the example of dP${}_2$ theory. Along the way, we also offer a general field theory proof of the odd shift of electric charge on Sp$(k{)}_{\pi }$ instanton solitons, previously observed via geometric engineering for low-rank supersymmetric theories.

77 pages, 28 figures

References in corpus (7)

• Witten Index and Wall Crossing
• A Farey Tail for Attractor Black Holes
• The M5-Brane Elliptic Genus: Modularity and BPS States
• Topological Strings and (Almost) Modular Forms
• Examples of M5-Brane Elliptic Genera
• 5D BPS Quivers and KK Towers
• Magnetic discrete gauge field in the confining vacua and the supersymmetric index

Cited by in corpus (5)

• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• Seiberg-Witten curves with O7${}^{\pm }$-planes
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• No room for minimal monopole dark matter