Gradient Properties of Perturbative Multiscalar RG Flows to Six Loops
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| Format: | Preprint |
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2024
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| _version_ | 1866911869900423168 |
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| author | Pannell, William H. Stergiou, Andreas |
| author_facet | Pannell, William H. Stergiou, Andreas |
| contents | The gradient property of the renormalisation group (RG) flow of multiscalar theories is examined perturbatively in $d=4$ and $d=4-\varepsilon$ dimensions. Such theories undergo RG flows in the space of quartic couplings $λ^I$. Starting at five loops, the relevant vector field that determines the physical RG flow is not the beta function traditionally computed in a minimal subtraction scheme in dimensional regularisation, but a suitable modification of it, the $B$ function. It is found that up to five loops the $B$ vector field is gradient, i.e. $B^I=G^{IJ}\partial A / \partialλ^J$ with $A$ a scalar and $G_{IJ}$ a rank-two symmetric tensor of the couplings. Up to five loops the beta function is also gradient, but it fails to be so at six loops. The conditions under which the $B$ function (and hence the RG flow) is gradient at six loops are specified, but their verification rests on a separate six-loop computation that remains to be performed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_17817 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient Properties of Perturbative Multiscalar RG Flows to Six Loops Pannell, William H. Stergiou, Andreas High Energy Physics - Theory Statistical Mechanics High Energy Physics - Phenomenology The gradient property of the renormalisation group (RG) flow of multiscalar theories is examined perturbatively in $d=4$ and $d=4-\varepsilon$ dimensions. Such theories undergo RG flows in the space of quartic couplings $λ^I$. Starting at five loops, the relevant vector field that determines the physical RG flow is not the beta function traditionally computed in a minimal subtraction scheme in dimensional regularisation, but a suitable modification of it, the $B$ function. It is found that up to five loops the $B$ vector field is gradient, i.e. $B^I=G^{IJ}\partial A / \partialλ^J$ with $A$ a scalar and $G_{IJ}$ a rank-two symmetric tensor of the couplings. Up to five loops the beta function is also gradient, but it fails to be so at six loops. The conditions under which the $B$ function (and hence the RG flow) is gradient at six loops are specified, but their verification rests on a separate six-loop computation that remains to be performed. |
| title | Gradient Properties of Perturbative Multiscalar RG Flows to Six Loops |
| topic | High Energy Physics - Theory Statistical Mechanics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2402.17817 |