Unified Structural Embedding of Orbifold Sigma Models
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915626355785728 |
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| author | D'Agostino, Francesco |
| author_facet | D'Agostino, Francesco |
| contents | This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat such sectors separately, requiring ad hoc regularizations near singularities and failing at capturing inter-sector interactions under renormalization group flow. Therefore, the scope of this study aims at resolving these limitations through the construction of a unified orbifold algebra $\mathcal{A}(X/G)$ that decomposes into idempotent-projected components corresponding to conjugacy classes of the finite group $G$ acting on the target space $X$. The formalism is shown to recover conventional sigma model results in the smooth limit where $G$ approaches the trivial group, with the internal renormalization group derivation reducing to the standard one-loop beta function proportional to the Ricci tensor. Examples demonstrate the applicability, including explicit calculations for the $\mathbb{C}/\mathbb{Z}_2$ orbifold that exhibit the decomposition into untwisted and twisted field contributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13476 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unified Structural Embedding of Orbifold Sigma Models D'Agostino, Francesco Mathematical Physics Quantum Physics This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat such sectors separately, requiring ad hoc regularizations near singularities and failing at capturing inter-sector interactions under renormalization group flow. Therefore, the scope of this study aims at resolving these limitations through the construction of a unified orbifold algebra $\mathcal{A}(X/G)$ that decomposes into idempotent-projected components corresponding to conjugacy classes of the finite group $G$ acting on the target space $X$. The formalism is shown to recover conventional sigma model results in the smooth limit where $G$ approaches the trivial group, with the internal renormalization group derivation reducing to the standard one-loop beta function proportional to the Ricci tensor. Examples demonstrate the applicability, including explicit calculations for the $\mathbb{C}/\mathbb{Z}_2$ orbifold that exhibit the decomposition into untwisted and twisted field contributions. |
| title | Unified Structural Embedding of Orbifold Sigma Models |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2505.13476 |