Doubled α'-Geometry

TL;DR

The paper tackles how to incorporate $\alpha'$ corrections into a duality-covariant description of the massless sector of oriented bosonic closed strings by formulating a doubled-field theory with left-moving $D+D$ bosons that realize $O(D,D)$ symmetry. It develops a doubled conformal field theory with a strong constraint, introduces Virasoro-like operators ${\cal S}$ and ${\cal T}$ built from a doubled metric ${\cal M}^{MN}$ and a dilaton, and derives $\alpha'$-corrected gauge algebras through a quantum $C$-bracket and its $O(D,D)$-covariantization, culminating in a cubic, gauge-invariant action $S$ expressed via a star-product. The key contributions include explicit constructions of the inner product and brackets with $\alpha'$ terms, a divergence-free tensor formalism, and a consistent truncation that reproduces the two-derivative massless action while encoding higher-derivative corrections up to finite order. This framework provides a self-contained, duality-covariant approach to $\alpha'$ corrections for massless string fields with potential connections to string field theory and nonlocal stringy effects.

Abstract

We develop doubled-coordinate field theory to determine the α' corrections to the massless sector of oriented bosonic closed string theory. Our key tool is a string current algebra of free left-handed bosons that makes O(D,D) T-duality manifest. While T-dualities are unchanged, diffeomorphisms and b-field gauge transformations receive corrections, with a gauge algebra given by an α'-deformation of the duality-covariantized Courant bracket. The action is cubic in a double metric field, an unconstrained extension of the generalized metric that encodes the gravitational fields. Our approach provides a consistent truncation of string theory to massless fields with corrections that close at finite order in α'.