Non-trivial fixed point of a $ψ^4_d$ fermionic theory, II. Anomalous exponent and scaling operators
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909876799668224 |
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| author | Giuliani, Alessandro Mastropietro, Vieri Rychkov, Slava Scola, Giuseppe |
| author_facet | Giuliani, Alessandro Mastropietro, Vieri Rychkov, Slava Scola, Giuseppe |
| contents | We consider the Renormalization Group (RG) fixed-point theory associated with a fermionic $ψ^4_d$ model in $d=1,2,3$ with fractional kinetic term, whose scaling dimension is fixed so that the quartic interaction is weakly relevant in the RG sense. The model is defined in terms of a Grassmann functional integral with interaction $V^*$, solving a fixed-point RG equation in the presence of external fields, and a fixed ultraviolet cutoff. We define and construct the field and density scale-invariant response functions, and prove that the critical exponent of the former is the naive one, while that of the latter is anomalous and analytic. We construct the corresponding (almost-)scaling operators, whose two point correlations are scale-invariant up to a remainder term, which decays like a stretched exponential at distances larger than the inverse of the ultraviolet cutoff. Our proof is based on constructive RG methods and, specifically, on a convergent tree expansion for the generating function of correlations, which generalizes the approach developed by three of the authors in a previous publication [A. Giuliani, V. Mastropietro, S. Rychkov, JHEP 01 (2021) 026]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14904 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-trivial fixed point of a $ψ^4_d$ fermionic theory, II. Anomalous exponent and scaling operators Giuliani, Alessandro Mastropietro, Vieri Rychkov, Slava Scola, Giuseppe Mathematical Physics High Energy Physics - Theory We consider the Renormalization Group (RG) fixed-point theory associated with a fermionic $ψ^4_d$ model in $d=1,2,3$ with fractional kinetic term, whose scaling dimension is fixed so that the quartic interaction is weakly relevant in the RG sense. The model is defined in terms of a Grassmann functional integral with interaction $V^*$, solving a fixed-point RG equation in the presence of external fields, and a fixed ultraviolet cutoff. We define and construct the field and density scale-invariant response functions, and prove that the critical exponent of the former is the naive one, while that of the latter is anomalous and analytic. We construct the corresponding (almost-)scaling operators, whose two point correlations are scale-invariant up to a remainder term, which decays like a stretched exponential at distances larger than the inverse of the ultraviolet cutoff. Our proof is based on constructive RG methods and, specifically, on a convergent tree expansion for the generating function of correlations, which generalizes the approach developed by three of the authors in a previous publication [A. Giuliani, V. Mastropietro, S. Rychkov, JHEP 01 (2021) 026]. |
| title | Non-trivial fixed point of a $ψ^4_d$ fermionic theory, II. Anomalous exponent and scaling operators |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.14904 |