Generalised symmetries and state-operator correspondence for nonlocal operators
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| Format: | Preprint |
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2024
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| author | Hofman, Diego M. Vitouladitis, Stathis |
| author_facet | Hofman, Diego M. Vitouladitis, Stathis |
| contents | We provide a one-to-one correspondence between line operators and states in four-dimensional CFTs with continuous 1-form symmetries. In analogy with 0-form symmetries in two dimensions, such CFTs have a free photon realisation and enjoy an infinite-dimensional current algebra that generalises the familiar Kac-Moody algebras. We construct the representation theory of this current algebra, which allows for a full description of the space of states on an arbitrary closed spatial slice. On $\mathbb{S}^2\times\mathbb{S}^1$, we rederive the spectrum by performing a path integral on $\mathbb{B}^3\times\mathbb{S}^1$ with insertions of line operators. This leads to a direct and explicit correspondence between the line operators of the theory and the states on $\mathbb{S}^2\times\mathbb{S}^1$. Interestingly, we find that the vacuum state is not prepared by the empty path integral but by a squeezing operator. Additionally, we generalise some of our results in two directions. Firstly, we construct current algebras in $(2p+2)$-dimensional CFTs, that are universal whenever the theory has a $p$-form symmetry, and secondly we provide a non-invertible generalisation of those higher-dimensional current algebras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_02662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalised symmetries and state-operator correspondence for nonlocal operators Hofman, Diego M. Vitouladitis, Stathis High Energy Physics - Theory We provide a one-to-one correspondence between line operators and states in four-dimensional CFTs with continuous 1-form symmetries. In analogy with 0-form symmetries in two dimensions, such CFTs have a free photon realisation and enjoy an infinite-dimensional current algebra that generalises the familiar Kac-Moody algebras. We construct the representation theory of this current algebra, which allows for a full description of the space of states on an arbitrary closed spatial slice. On $\mathbb{S}^2\times\mathbb{S}^1$, we rederive the spectrum by performing a path integral on $\mathbb{B}^3\times\mathbb{S}^1$ with insertions of line operators. This leads to a direct and explicit correspondence between the line operators of the theory and the states on $\mathbb{S}^2\times\mathbb{S}^1$. Interestingly, we find that the vacuum state is not prepared by the empty path integral but by a squeezing operator. Additionally, we generalise some of our results in two directions. Firstly, we construct current algebras in $(2p+2)$-dimensional CFTs, that are universal whenever the theory has a $p$-form symmetry, and secondly we provide a non-invertible generalisation of those higher-dimensional current algebras. |
| title | Generalised symmetries and state-operator correspondence for nonlocal operators |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.02662 |