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arXiv · 2505.13476

Unified Structural Embedding of Orbifold Sigma Models

Francesco D'Agostino
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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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Francesco D'Agostino. 2025-05-09. Unified Structural Embedding of Orbifold Sigma Models. https://doi.org/10.5281/zenodo.15376431

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