Dynamical Generation of the VY Superpotential in $N=1$ SYM: A Higher-Form Perspective
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914467512582144 |
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| author | Gu, Wei |
| author_facet | Gu, Wei |
| contents | We present a semiclassical account of the Veneziano-Yankielowicz (VY) superpotential in four-dimensional $N=1$ super Yang-Mills theory. Motivated by two-dimensional gauged linear sigma models, where superpotentials arise from vortex dynamics, we reinterpret domain walls as fundamental objects associated with higher-form gauge fields. In this formulation, the vacuum structure is encoded in a compact three-form gauge field, whose four-form flux labels topological sectors. In the presence of charged matter with total charge $N$, these sectors exhibit a natural $\mathbb{Z}_N$ structure, leading to a decomposition into $N$ semiclassical contributions. These contributions arise from Euclidean point-like configurations in the higher-form sector, analogous to fractional instantons. We show that these configurations provide the relevant non-perturbative contributions to the effective superpotential. Integrating out the associated degrees of freedom reproduces the VY superpotential in the infrared. This gives a semiclassical origin of the VY superpotential in terms of higher-form gauge dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10919 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamical Generation of the VY Superpotential in $N=1$ SYM: A Higher-Form Perspective Gu, Wei High Energy Physics - Theory We present a semiclassical account of the Veneziano-Yankielowicz (VY) superpotential in four-dimensional $N=1$ super Yang-Mills theory. Motivated by two-dimensional gauged linear sigma models, where superpotentials arise from vortex dynamics, we reinterpret domain walls as fundamental objects associated with higher-form gauge fields. In this formulation, the vacuum structure is encoded in a compact three-form gauge field, whose four-form flux labels topological sectors. In the presence of charged matter with total charge $N$, these sectors exhibit a natural $\mathbb{Z}_N$ structure, leading to a decomposition into $N$ semiclassical contributions. These contributions arise from Euclidean point-like configurations in the higher-form sector, analogous to fractional instantons. We show that these configurations provide the relevant non-perturbative contributions to the effective superpotential. Integrating out the associated degrees of freedom reproduces the VY superpotential in the infrared. This gives a semiclassical origin of the VY superpotential in terms of higher-form gauge dynamics. |
| title | Dynamical Generation of the VY Superpotential in $N=1$ SYM: A Higher-Form Perspective |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.10919 |