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| Format: | Recurso digital |
| Language: | English |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17811472 |
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| _version_ | 1866901853765107712 |
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| author | Janik, John |
| author_facet | Janik, John |
| contents | <p>We develop the sphere partition function within the framework of $E_8$ modular spacetime, where four-dimensional Lorentzian geometry emerges from the modular structure of a hyperfinite type~$\mathrm{III}_1$ factor with outer $E_8$ symmetry. The sphere partition function $Z(S^d)$ serves as a gauge-invariant, systematically calculable observable that bridges microscopic noncommutative data and macroscopic emergent geometry. We establish the mathematical foundations for its computation using split-regularized spectral functionals, demonstrate how it encodes the conformal anomaly coefficients recoverable from relative entropy, and provide explicit computational strategies leveraging the $E_8$ representation structure. Since the noncommutative deformation breaks supersymmetry, exact supersymmetric localization applies only to the vector sector (the 248 gauge fields) in the commutative limit; the matter sector (128 fermions and 28 scalars) must be computed via heat kernel and conformal perturbation methods. The partition function emerges as a consistency test for the reconstruction theorem: the value computed directly from the noncommutative torus algebra $A_\theta$ must agree with that obtained from the reconstructed metric via standard conformal field theory methods.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17811472 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Conformal Anomaly of $E_8$ Modular Spacetime Janik, John sphere partition function modular theory AQFT gauge invariant <p>We develop the sphere partition function within the framework of $E_8$ modular spacetime, where four-dimensional Lorentzian geometry emerges from the modular structure of a hyperfinite type~$\mathrm{III}_1$ factor with outer $E_8$ symmetry. The sphere partition function $Z(S^d)$ serves as a gauge-invariant, systematically calculable observable that bridges microscopic noncommutative data and macroscopic emergent geometry. We establish the mathematical foundations for its computation using split-regularized spectral functionals, demonstrate how it encodes the conformal anomaly coefficients recoverable from relative entropy, and provide explicit computational strategies leveraging the $E_8$ representation structure. Since the noncommutative deformation breaks supersymmetry, exact supersymmetric localization applies only to the vector sector (the 248 gauge fields) in the commutative limit; the matter sector (128 fermions and 28 scalars) must be computed via heat kernel and conformal perturbation methods. The partition function emerges as a consistency test for the reconstruction theorem: the value computed directly from the noncommutative torus algebra $A_\theta$ must agree with that obtained from the reconstructed metric via standard conformal field theory methods.</p> |
| title | The Conformal Anomaly of $E_8$ Modular Spacetime |
| topic | sphere partition function modular theory AQFT gauge invariant |
| url | https://doi.org/10.5281/zenodo.17811472 |