arXiv 2111.094482021-11-17hep-th

$\mathbb{S}^1$的5维Seiberg-Witten理论

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

Qiang Jia, Piljin Yi

备注：: 77 pages, 28 figures
DOI：: 10.1007/JHEP02(2022)125

摘要：

本文研究了在$\mathbb{S}^1$上紧致化的5dPDMATHABMM Yang-Mills理论的红外物理性质，并着眼于4d和5d极限.最简单的库仑模空间的全球结构的概述，重点是如何多个平面四维Seiberg-Witten几何嵌入在雪茄几何的一个单一的5D理论$\mathbb{S}^1$。库仑相界的解压缩限制给予特别的关注，并涉及到如何通过5D BPS粒子的壁交叉关闭。另一方面，BPS磁弦的椭圆属也能穿越壁面，并保留了4d穿越壁面的记忆，我们以dP $_2$理论为例对此进行了讨论.一路上，我们还提供了一个一般的场论证明的奇数移位的电荷Sp $(k)_π$瞬子孤子，以前观察到通过几何工程的低秩超对称理论。

英文摘要：

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$(k)_π$ instanton solitons, previously observed via geometric engineering for low-rank supersymmetric theories.

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英文摘要：

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