2D black holes, Bianchi I cosmologies, and 𝛼′

We report two surprising results on 𝛼′ corrections in string theory restricted to massless fields. First, for critical dimension Bianchi type I cosmologies with 𝑞 scale factors only 𝑞 −1 of them have nontrivial 𝛼′ corrections. In particular, for Friedmann-Robertson-Walker backgrounds all 𝛼′ corrections are trivial. Second, in noncritical dimensions, all terms in the spacetime action other than the cosmological term are field redefinition equivalent to terms with arbitrarily many derivatives, with the latter generally of the same order. Assuming an 𝛼′ expansion with coefficients that fall off sufficiently fast, we consider field redefinitions consistent with this falloff and classify the higher-derivative terms for two-dimensional string theory with one timelike isometry. This most general duality-invariant theory permits black-hole solutions, and we provide perturbative and nonperturbative tools to explore them.