One-Loop Renormalization of Anisotropic Two-Scalar Quantum Field Theories
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Ageev, Dmitry S. Ageeva, Yulia A. |
| author_facet | Ageev, Dmitry S. Ageeva, Yulia A. |
| contents | We develop a basis--covariant one--loop renormalization framework for two interacting real scalars in $D=4-ε$ with the most general two--derivative Lorentz--violating quadratic form, allowing anisotropic spatial gradients and direction--dependent kinetic mixing, together with general cubic and quartic interactions forming RG complete set of operators at one-loop. In dimensional regularization with minimal subtraction we compute the full set of one--loop UV divergences and obtain closed beta functions for quartic and cubic couplings, masses.
The pole coefficients admit a universal spectral representation as angular averages over the direction--dependent eigenvalues and projectors of the UV kinetic matrix; all anisotropy dependence enters through a single universal kernel admitting two--particle phase--space interpretation. We classify fixed points and fixed manifolds and show, in particular, that anisotropy restricts the existence of the coupled Wilson--Fisher--type fixed point. When the cross--gradients are turned on the coefficients in beta functions are governed by six phase--space weights admitting interpretation in terms of encoding ``populations'' and ``coherences'' of the UV normal modes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-Loop Renormalization of Anisotropic Two-Scalar Quantum Field Theories Ageev, Dmitry S. Ageeva, Yulia A. High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology We develop a basis--covariant one--loop renormalization framework for two interacting real scalars in $D=4-ε$ with the most general two--derivative Lorentz--violating quadratic form, allowing anisotropic spatial gradients and direction--dependent kinetic mixing, together with general cubic and quartic interactions forming RG complete set of operators at one-loop. In dimensional regularization with minimal subtraction we compute the full set of one--loop UV divergences and obtain closed beta functions for quartic and cubic couplings, masses. The pole coefficients admit a universal spectral representation as angular averages over the direction--dependent eigenvalues and projectors of the UV kinetic matrix; all anisotropy dependence enters through a single universal kernel admitting two--particle phase--space interpretation. We classify fixed points and fixed manifolds and show, in particular, that anisotropy restricts the existence of the coupled Wilson--Fisher--type fixed point. When the cross--gradients are turned on the coefficients in beta functions are governed by six phase--space weights admitting interpretation in terms of encoding ``populations'' and ``coherences'' of the UV normal modes. |
| title | One-Loop Renormalization of Anisotropic Two-Scalar Quantum Field Theories |
| topic | High Energy Physics - Theory Strongly Correlated Electrons High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.19670 |