Unified Structural Embedding of Orbifold Sigma Models

• URL: http://arxiv.org/abs/2505.13476v2
• Date: Thu, 29 May 2025 00:30:19 GMT
• Title: Unified Structural Embedding of Orbifold Sigma Models
• Authors: Francesco D'Agostino,
• Abstract summary: This study introduces a new unified structural framework for orbifold sigma models.<n>The formalism is shown to recover conventional sigma model results in the smooth limit where $G$ approaches the trivial group.<n>Examples demonstrate the applicability, including explicit calculations for the $mathbbC/mathbbZ$ orbifold.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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