Lattice construction of mixed 't Hooft anomaly with higher-form symmetry
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910285189611520 |
|---|---|
| author | Abe, Motokazu Morikawa, Okuto Onoda, Soma Suzuki, Hiroshi Tanizaki, Yuya |
| author_facet | Abe, Motokazu Morikawa, Okuto Onoda, Soma Suzuki, Hiroshi Tanizaki, Yuya |
| contents | In this talk, we give the lattice regularized formulation of the mixed 't Hooft anomaly between the $\mathbb{Z}_N$ $1$-form symmetry and the $θ$ periodicity for $4$d pure Yang-Mills theory, which was originally discussed by Gaiotto $\textit{et al.}$ in the continuum description. For this purpose, we define the topological charge of the lattice $SU(N)$ gauge theory coupled with the background $\mathbb{Z}_N$ $2$-form gauge fields $B_p$ by generalizing Lüscher's construction of the $SU(N)$ topological charge. We show that this lattice topological charge enjoys the fractional $1/N$ shift completely characterized by the background gauge field $B_p$, and this rigorously proves the mixed 't Hooft anomaly with the finite lattice spacings. As a consequence, the Yang-Mills vacua at $θ$ and $θ+2π$ are distinct as the symmetry-protected topological states when the confinement is assumed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00495 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lattice construction of mixed 't Hooft anomaly with higher-form symmetry Abe, Motokazu Morikawa, Okuto Onoda, Soma Suzuki, Hiroshi Tanizaki, Yuya High Energy Physics - Lattice In this talk, we give the lattice regularized formulation of the mixed 't Hooft anomaly between the $\mathbb{Z}_N$ $1$-form symmetry and the $θ$ periodicity for $4$d pure Yang-Mills theory, which was originally discussed by Gaiotto $\textit{et al.}$ in the continuum description. For this purpose, we define the topological charge of the lattice $SU(N)$ gauge theory coupled with the background $\mathbb{Z}_N$ $2$-form gauge fields $B_p$ by generalizing Lüscher's construction of the $SU(N)$ topological charge. We show that this lattice topological charge enjoys the fractional $1/N$ shift completely characterized by the background gauge field $B_p$, and this rigorously proves the mixed 't Hooft anomaly with the finite lattice spacings. As a consequence, the Yang-Mills vacua at $θ$ and $θ+2π$ are distinct as the symmetry-protected topological states when the confinement is assumed. |
| title | Lattice construction of mixed 't Hooft anomaly with higher-form symmetry |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2401.00495 |