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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.21143 |
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Table of Contents:
- We construct a fully covariant,$\mathbf{O}(D,D)$-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 $\mathbf{O}(D,D)$-symmetric gravitational-wave equations for the massless sector, governs the tachyon and all massive modes, and clarifies how higher excitations contribute to $α^{\prime}$-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 $\mathbf{O}(D,D)$ 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 $\mathbf{O}(D,D)$ symmetry and doubled diffeomorphisms remain exact and undeformed at the fundamental level of string theory.