Universal box operator: O(D, D)-symmetry and α′-corrections

초록

We construct a fully covariant, O (D, D)-symmetric d’Alembertian—or box operator—that acts on tensor fields of arbitrary rank and provides a universal kinetic term for all bosonic closed-string states. In its Riemannian parametrization, the operator packages the Riemann curvature, H -flux, and dilaton gradient into a single duality-covariant object. This yields O (D, D)-symmetric gravitational-wave equations for the massless sector, governs the tachyon and all massive modes, and clarifies how higher excitations contribute to α ′-corrections. The box operator thus supplies a unified description of closed-string dynamics across the entire spectrum. Our analysis shows that any apparent breaking of O (D, D) symmetry arises only after integrating out massive modes in a Wilsonian sense, where loop momentum integrals obscure half of the doubled momenta. We stand on the view that O (D, D) symmetry and doubled diffeomorphisms remain exact and undeformed at the fundamental level of string theory.

키워드