No abstract

We determine the complete spacetime action to first order in α ′ for the massless fields of bosonic string theory compactified on a d-dimensional torus. A fully systematic procedure is developed that brings the action into a minimal form in which all fields apart from the metric enter only with first-order derivatives. T-duality implies that this action must have a global O(d, d, R) symmetry, and we show that this requires a Green-Schwarz type mechanism for α ′ -deformed O(d, d, R) transformations. In terms of a frame formalism with GL(d) × GL(d) gauge symmetry this amounts to a modification of the three-form curvature by a Chern-Simons term for composite gauge fields.

We use exceptional field theory to compute Kaluza-Klein mass spectra around {AdS_{3}}AdS3 vacua that sit in half-maximal gauged supergravity in three dimensions. The formalism applies to any vacuum that arises from a consistent truncation of higher-dimensional supergravity, no matter what symmetries are preserved. We illustrate its efficiency by computing the spectra of {N}=(2,0)N=(2,0) and {N}=(1,1)N=(1,1) six-dimensional supergravities on {AdS_{3}}\times S^{3}AdS3×S3 and of type II supergravity on {AdS_{3}}\times S^{3}\times S^{3}\times S^{1}AdS3×S3×S3×S1.