Non-Local Regularization of String Worldsheets and Calabi-Yau Singularities via Circular Product Integrals

We develop a fully covariant, ghost-free framework for the non-local regularization of string worldsheets and Calabi–Yau compactification spaces based on the Circular Product Integral (CPI). The CPI implements a finite non-locality scale through geometric averaging over geodesic circles, producing an entire, pole-free deformation of curvature invariants. When embedded into the Polyakov action, it enforces a UV-saturated curvature bound while preserving second-order dynamics, Weyl invariance up to a localized correction, and BRST nilpotency. Applied to Calabi–Yau threefolds, the CPI resolves conifold singularities without introducing new moduli or cycles, replacing the apex with a smooth finite-curvature core. The resulting four-dimensional effective theory exhibits an entire-function propagator free of ghosts and tachyons. Phenomenological implications include gravitational-wave echoes, moduli stabilization, and holographic smearing of bulk curvature.