Wreathing, Discrete Gauging, and Non-invertible Symmetries
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913663560974336 |
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| author | Grimminger, Julius F. Harding, William Mekareeya, Noppadol |
| author_facet | Grimminger, Julius F. Harding, William Mekareeya, Noppadol |
| contents | 't Hooft anomalies of discrete global symmetries and gaugings thereof have rich mathematical structures and far-reaching physical consequences. We examine each subgroup $G$, up to automorphisms, of the permutation group $S_4$ that acts on the four legs of the affine $D_4$ quiver diagram, which is mirror dual to the 3d $\mathcal{N}=4$ $\mathrm{SU}(2)$ gauge theory with four flavours. These actions are studied in terms of how each permutation cycle acts on the superconformal index of the theory in question. We present a prescription for refining the index with respect to the fugacities associated with the Abelian discrete symmetries that are subgroups of $G$. This allows us to study sequential gauging of various subgroups of $G$ and construct symmetry webs. We study the effects of 't Hooft anomalies and non-invertible symmetries that arise from discrete gauging on the index. When the whole symmetry $G$ is gauged, our results are in perfect agreement with a type of discrete operations on the quiver, known as wreathing, discussed in the literature. We provide a general prescription for computing the index for any wreathed quivers that contain unitary or special unitary gauge groups. We demonstrate this in an example of the 3d $\mathcal{N}=4$ $\mathrm{U}(N)$ gauge theory with $n$ flavours and compare the results with gauging the charge conjugation symmetry associated with the flavour symmetry of such a theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_12906 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wreathing, Discrete Gauging, and Non-invertible Symmetries Grimminger, Julius F. Harding, William Mekareeya, Noppadol High Energy Physics - Theory 't Hooft anomalies of discrete global symmetries and gaugings thereof have rich mathematical structures and far-reaching physical consequences. We examine each subgroup $G$, up to automorphisms, of the permutation group $S_4$ that acts on the four legs of the affine $D_4$ quiver diagram, which is mirror dual to the 3d $\mathcal{N}=4$ $\mathrm{SU}(2)$ gauge theory with four flavours. These actions are studied in terms of how each permutation cycle acts on the superconformal index of the theory in question. We present a prescription for refining the index with respect to the fugacities associated with the Abelian discrete symmetries that are subgroups of $G$. This allows us to study sequential gauging of various subgroups of $G$ and construct symmetry webs. We study the effects of 't Hooft anomalies and non-invertible symmetries that arise from discrete gauging on the index. When the whole symmetry $G$ is gauged, our results are in perfect agreement with a type of discrete operations on the quiver, known as wreathing, discussed in the literature. We provide a general prescription for computing the index for any wreathed quivers that contain unitary or special unitary gauge groups. We demonstrate this in an example of the 3d $\mathcal{N}=4$ $\mathrm{U}(N)$ gauge theory with $n$ flavours and compare the results with gauging the charge conjugation symmetry associated with the flavour symmetry of such a theory. |
| title | Wreathing, Discrete Gauging, and Non-invertible Symmetries |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2410.12906 |