Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929399256842240 |
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| author | Delamotte, Bertrand De Polsi, Gonzalo Tissier, Matthieu Wschebor, Nicolás |
| author_facet | Delamotte, Bertrand De Polsi, Gonzalo Tissier, Matthieu Wschebor, Nicolás |
| contents | It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead to a better understanding of the critical physics or improve approximation schemes. However, within the framework of the non-perturbative or functional renormalization group and, in particular, of one of its most used approximation schemes, the Derivative Expansion (DE), non-trivial constraints only apply from third order (usually denoted $\mathcal{O}(\partial^4)$), at least in the usual formulation of the DE that includes correlation functions involving only the order parameter. In this work, we implement conformal constraints on a generalized DE including composite operators and show that new constraints already appear at second order of the DE (or $\mathcal{O}(\partial^2)$). We show how these constraints can be used to fix nonphysical regulator parameters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_02517 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group Delamotte, Bertrand De Polsi, Gonzalo Tissier, Matthieu Wschebor, Nicolás Statistical Mechanics High Energy Physics - Theory It is expected that conformal symmetry is an emergent property of many systems at their critical point. This imposes strong constraints on the critical behavior of a given system. Taking them into account in theoretical approaches can lead to a better understanding of the critical physics or improve approximation schemes. However, within the framework of the non-perturbative or functional renormalization group and, in particular, of one of its most used approximation schemes, the Derivative Expansion (DE), non-trivial constraints only apply from third order (usually denoted $\mathcal{O}(\partial^4)$), at least in the usual formulation of the DE that includes correlation functions involving only the order parameter. In this work, we implement conformal constraints on a generalized DE including composite operators and show that new constraints already appear at second order of the DE (or $\mathcal{O}(\partial^2)$). We show how these constraints can be used to fix nonphysical regulator parameters. |
| title | Conformal invariance and composite operators: A strategy for improving the derivative expansion of the nonperturbative renormalization group |
| topic | Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.02517 |