Universal Box Operator: $\mathbf{O}(D,D)$-Symmetry and $α^{\prime}$-Corrections

Kawon Lee; Jeong-Hyuck Park

doi:10.1016/j.physletb.2025.140116

paper

Universal Box Operator: $O (D, D)$ -Symmetry and $α^{'}$ -Corrections

arXiv:2506.21143 · doi:10.1016/j.physletb.2025.140116

Abstract

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.

arXiv commentVersion 2: Final version of publication, Title changed, 7 pages plus 9 pages of Supplementary Material

Universal Box Operator: O(D,D)-Symmetry and α′-Corrections

Abstract

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Universal Box Operator: $O (D, D)$ -Symmetry and $α^{'}$ -Corrections