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| Format: | Preprint |
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2022
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| Online Access: | https://arxiv.org/abs/2211.10347 |
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| _version_ | 1866913278658084864 |
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| author | Poppitz, Erich Wandler, F David |
| author_facet | Poppitz, Erich Wandler, F David |
| contents | We study two semiclassical limits of $SU(2)$ Yang-Mills theory on a spatial torus with a 't Hooft twist: the ``femtouniverse,'' where all $\mathbb{T}^3$ directions are small, and deformed Yang-Mills theory on $\mathbb{T}^2 \times \mathbb{S}^1$, with small $\mathbb{S}^1$ and large or infinite $\mathbb{T}^2$. Carefully defining the symmetries, we show that the classical ground states, while different, have the same transformation properties under the 1-form center symmetry and parity. We argue that this is behind the identical multi-branch $θ$-dependent vacuum structure of these theories. We then calculate the one-loop potential for the $\mathbb{S}^1$-holonomy in the presence of twists on $\mathbb{T}^2$. We use it to study the quantum stability of the semiclassical ground states in gauge theories with massive or massless adjoint fermions on spatial $\mathbb{T}^2 \times \mathbb{S}^1$, with a twist in the $\mathbb{T}^2$. The results point towards some interesting features worthy of further study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_10347 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Gauge theory geography: charting a path between semiclassical islands Poppitz, Erich Wandler, F David High Energy Physics - Theory High Energy Physics - Lattice We study two semiclassical limits of $SU(2)$ Yang-Mills theory on a spatial torus with a 't Hooft twist: the ``femtouniverse,'' where all $\mathbb{T}^3$ directions are small, and deformed Yang-Mills theory on $\mathbb{T}^2 \times \mathbb{S}^1$, with small $\mathbb{S}^1$ and large or infinite $\mathbb{T}^2$. Carefully defining the symmetries, we show that the classical ground states, while different, have the same transformation properties under the 1-form center symmetry and parity. We argue that this is behind the identical multi-branch $θ$-dependent vacuum structure of these theories. We then calculate the one-loop potential for the $\mathbb{S}^1$-holonomy in the presence of twists on $\mathbb{T}^2$. We use it to study the quantum stability of the semiclassical ground states in gauge theories with massive or massless adjoint fermions on spatial $\mathbb{T}^2 \times \mathbb{S}^1$, with a twist in the $\mathbb{T}^2$. The results point towards some interesting features worthy of further study. |
| title | Gauge theory geography: charting a path between semiclassical islands |
| topic | High Energy Physics - Theory High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2211.10347 |