On the UV/IR mixing of Lie algebra-type noncommutatitive $ϕ^4$-theories
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929330218598400 |
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| author | Hersent, Kilian |
| author_facet | Hersent, Kilian |
| contents | We show that a UV divergence of the propagator integral implies the divergences of the UV/IR mixing in the two-point function at one-loop for a $ϕ^4$-theory on a generic Lie algebra-type noncommutative space-time. The UV/IR mixing is defined as a UV divergence of the planar contribution and an IR singularity of the non-planar contribution, the latter being due to the former UV divergence, and the UV finiteness of the non-planar contribution. Some properties of this general treatment are discussed. The UV finiteness of the non-planar contribution and the renormalizability of the theory are not treated but commented. Applications are performed for the Moyal space, having a UV/IR mixing, and the $κ$-Minkowski space for which the two-point function at one-loop is finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08917 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the UV/IR mixing of Lie algebra-type noncommutatitive $ϕ^4$-theories Hersent, Kilian High Energy Physics - Theory Mathematical Physics We show that a UV divergence of the propagator integral implies the divergences of the UV/IR mixing in the two-point function at one-loop for a $ϕ^4$-theory on a generic Lie algebra-type noncommutative space-time. The UV/IR mixing is defined as a UV divergence of the planar contribution and an IR singularity of the non-planar contribution, the latter being due to the former UV divergence, and the UV finiteness of the non-planar contribution. Some properties of this general treatment are discussed. The UV finiteness of the non-planar contribution and the renormalizability of the theory are not treated but commented. Applications are performed for the Moyal space, having a UV/IR mixing, and the $κ$-Minkowski space for which the two-point function at one-loop is finite. |
| title | On the UV/IR mixing of Lie algebra-type noncommutatitive $ϕ^4$-theories |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2309.08917 |