Arc Theory v23: Extremal CFT Uniqueness, Rademacher Regularization, and Geometric Classification of Modular Saddles

Arcman

Arc Theory v23: Extremal CFT Uniqueness, Rademacher Regularization, and Geometric Classification of Modular Saddles

https://doi.org/10.5281/zenodo.18895656

Creators: Arcman

Resource Type: Preprint / Working Paper

Description:
We analyze the uniqueness of extremal conformal field theories under modularinvariance and sparsity conditions. While the uniqueness of the partition function can be established, the general existence remains open beyond low levels. We further study the convergence of the Poincaré series representation of the partition function via Rademacher regularization. Finally, we classify non-perturbative handlebody saddles of three-dimensional AdS gravity via modular group orbits.

Notes on v23:
This manuscript explicitly addresses the analytical obstruction in the large-central-charge regime. It includes rigorous mathematical annotations on the unitarity constraints on Fourier coefficients for extremal CFTs (with $k > 3$) and details the analytical continuation ofthe regularized Niebur-Poincaré series via Kloosterman sums and modified Bessel functions.

Keywords:
Extremal Conformal Field Theory; Modular Invariance; RademacherRegularization; AdS3 Gravity; Quantum Gravity; Arc Theory; Arc Geometry.