2025/05/09 by D'Agostino, Francesco
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2505.13476
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 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 ℂ/ℤ2 orbifold that exhibit the decomposition into untwisted and twisted field contributions.