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Aspects of 5d Seiberg-Witten Theories on $\mathbb{S}^1$
- Publication Year :
- 2021
-
Abstract
- We study the infrared physics of 5d $\cal N=1$ 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.<br />Comment: 77 pages, 28 figures
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2111.09448
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP02(2022)125