Unified Structural Embedding of Orbifold Sigma Models

Fuente: arXiv
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Autore principale: D'Agostino, Francesco
Natura: Preprint
Pubblicazione: 2025
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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