Gravitational Topological Susceptibility and the Origin of a 1/ζ Mass Correction

We demonstrate that a negative mass correction δm2∝−1/ζδm2∝−1/ζ, necessary for vacuum energy cancellation in effective field theories with a Chern–Simons coupling aRR~aRR~ and a stabilizer term ζ(RR~)2ζ(RR~)2, arises naturally from the topological structure of the gravitational sector. Perturbative loops generate only positive powers of ζζ and cannot produce the required 1/ζ1/ζ dependence. By dualizing the stabilizer operator via a 4‑form field, we show that the effective axion mass receives a contribution proportional to the gravitational topological susceptibility χgrav=∫d4x⟨(RR~)(x)(RR~)(0)⟩χgrav=∫d4x⟨(RR~)(x)(RR~)(0)⟩. When χgrav∼MPl4/ζχgrav∼MPl4/ζ (as expected from non‑perturbative topological configurations such as gravitational instantons or wormholes), the induced δm2δm2 exactly cancels the positive vacuum energy terms, removing the need for fine‑tuning.

This mechanism is independent of the UV completion and provides a concrete, testable framework for understanding the smallness of the effective cosmological constant within a Chern–Simons axion model. The results have direct implications for cosmic birefringence, parity‑violating gravitational waves, and correlations in the cosmic microwave background.

effective field theory, Chern–Simons, axion, gravitational topological susceptibility, 4‑form, dualization, vacuum energy cancellation, cosmological constant problem, non‑perturbative quantum gravity, gravitational instantons, wormholes, parity violation, cosmic birefringence, RR~RR~ operator, stabilizer term, fine‑tuning, Hubble tension, dark energy, CMB polarization, gravitational waves, helicity asymmetry, TB/EB correlations, LiteBIRD, CMB‑S4, LISA, Euclid, DESI, axiverse, string theory, quantum gravity phenomenology.