UV Structure and Asymptotic Freedom of the 4D Sigma Model on Sp(2N,R)/U(N) with Fisher–Bures Metric
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2026
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| _version_ | 1866901148401664000 |
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| author | caldini, ignacio |
| author_facet | caldini, ignacio |
| contents | <p>We establish the ultraviolet structure of the four-dimensional nonlinear sigma model with target manifold M = Sp(2N,R)/U(N) equipped with the Fisher–Bures metric. The model arises in the Vacuum Time Geometry programme, where spacetime geometry emerges from the entanglement structure of the vacuum via a Page–Wootters mechanism, and the spacetime metric is the pullback of the quantum Fisher–Bures metric through an entanglement map λ : M4 →M.<br>We prove three main results. Theorem 1 gives the exact two-loop coefficient c1(N) = [N(N + 1)2 − 4]/[8(N + 1)2(N − 1)] for all N ≥ 2, with c1 → 1/8 as N → ∞. Theorem 2<br>establishes asymptotic freedom: the beta function satisfies β(T) < 0 for T ∈ (0, T∗), where T∗(d = 4,N = 28) ≈ 6.305, and the asymptotic freedom window does not collapse as N varies. Theorem 3 reports that three independent non-perturbative truncations of the Wetterich exact renormalization group equation yield β(T) < 0 for all T > 0, with no UV fixed point at finite coupling — a result strictly stronger than perturbative asymptotic freedom.<br>Asymptotic freedom follows from the negativity of the Ricci curvature, Ric < 0, which is itself a consequence of the non-negative sectional curvature KFB ≥ 0 of the Fisher–Bures metric on the symmetric space of noncompact type. The UV limit T → 0 corresponds, in the Page–Wootters framework, to the unentangled pure-state vacuum with flat spacetime geometry.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19664104 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | UV Structure and Asymptotic Freedom of the 4D Sigma Model on Sp(2N,R)/U(N) with Fisher–Bures Metric caldini, ignacio nonlinear sigma model asymptotic freedom Functional equations functional renormalization group symmetric spaces Quantum Theory quantum fisher information fisher bures metric Vacuum page wootters mechanism wetterich equation 81t17 53c35 81p45 <p>We establish the ultraviolet structure of the four-dimensional nonlinear sigma model with target manifold M = Sp(2N,R)/U(N) equipped with the Fisher–Bures metric. The model arises in the Vacuum Time Geometry programme, where spacetime geometry emerges from the entanglement structure of the vacuum via a Page–Wootters mechanism, and the spacetime metric is the pullback of the quantum Fisher–Bures metric through an entanglement map λ : M4 →M.<br>We prove three main results. Theorem 1 gives the exact two-loop coefficient c1(N) = [N(N + 1)2 − 4]/[8(N + 1)2(N − 1)] for all N ≥ 2, with c1 → 1/8 as N → ∞. Theorem 2<br>establishes asymptotic freedom: the beta function satisfies β(T) < 0 for T ∈ (0, T∗), where T∗(d = 4,N = 28) ≈ 6.305, and the asymptotic freedom window does not collapse as N varies. Theorem 3 reports that three independent non-perturbative truncations of the Wetterich exact renormalization group equation yield β(T) < 0 for all T > 0, with no UV fixed point at finite coupling — a result strictly stronger than perturbative asymptotic freedom.<br>Asymptotic freedom follows from the negativity of the Ricci curvature, Ric < 0, which is itself a consequence of the non-negative sectional curvature KFB ≥ 0 of the Fisher–Bures metric on the symmetric space of noncompact type. The UV limit T → 0 corresponds, in the Page–Wootters framework, to the unentangled pure-state vacuum with flat spacetime geometry.</p> |
| title | UV Structure and Asymptotic Freedom of the 4D Sigma Model on Sp(2N,R)/U(N) with Fisher–Bures Metric |
| topic | nonlinear sigma model asymptotic freedom Functional equations functional renormalization group symmetric spaces Quantum Theory quantum fisher information fisher bures metric Vacuum page wootters mechanism wetterich equation 81t17 53c35 81p45 |
| url | https://doi.org/10.5281/zenodo.19664104 |