Local operators in the Sine-Gordon model: $\partial_μϕ\, \partial_νϕ$ and the stress tensor
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2022
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| _version_ | 1866912338903302144 |
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| author | Fröb, Markus B. Cadamuro, Daniela |
| author_facet | Fröb, Markus B. Cadamuro, Daniela |
| contents | We consider the simplest non-trivial local composite operators in the massless Sine-Gordon model, which are $\partial_μϕ\, \partial_νϕ$ and the stress tensor $T_{μν}$. We show that even in the finite regime $β^2 < 4 π$ of the theory, these operators need additional renormalisation (beyond the free-field normal-ordering) at each order in perturbation theory. We further prove convergence of the renormalised perturbative series for their expectation values, both in the Euclidean signature and in Minkowski space-time, and for the latter in an arbitrary Hadamard state. Lastly, we show that one must add a quantum correction (proportional to $\hbar$) to the renormalised stress tensor to obtain a conserved quantity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_09223 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Local operators in the Sine-Gordon model: $\partial_μϕ\, \partial_νϕ$ and the stress tensor Fröb, Markus B. Cadamuro, Daniela Mathematical Physics High Energy Physics - Theory We consider the simplest non-trivial local composite operators in the massless Sine-Gordon model, which are $\partial_μϕ\, \partial_νϕ$ and the stress tensor $T_{μν}$. We show that even in the finite regime $β^2 < 4 π$ of the theory, these operators need additional renormalisation (beyond the free-field normal-ordering) at each order in perturbation theory. We further prove convergence of the renormalised perturbative series for their expectation values, both in the Euclidean signature and in Minkowski space-time, and for the latter in an arbitrary Hadamard state. Lastly, we show that one must add a quantum correction (proportional to $\hbar$) to the renormalised stress tensor to obtain a conserved quantity. |
| title | Local operators in the Sine-Gordon model: $\partial_μϕ\, \partial_νϕ$ and the stress tensor |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2205.09223 |