2D Black Holes, Bianchi I Cosmologies, and $\alpha'$

TL;DR

This paper investigates $$ corrections in string theory for specific cosmological backgrounds, revealing that only certain scale factors receive corrections and classifying higher derivative terms in two-dimensional string theory with black-hole solutions.

Contribution

It uncovers conditions under which $$ corrections are non-trivial in Bianchi I cosmologies and classifies higher derivative terms in 2D string theory with black-hole solutions.

Findings

In Bianchi I cosmologies, only $q-1$ scale factors have non-trivial $$ corrections.

All $$ corrections are trivial for FRW backgrounds.

The most general duality-invariant theory in 2D admits black-hole solutions.

Abstract

We report two surprising results on $\alpha'$ 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 non-trivial $\alpha'$ corrections. In particular, for FRW backgrounds all $\alpha'$ corrections are trivial. Second, in non-critical 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 $\alpha'$ expansion with coefficients that fall off sufficiently fast, we consider field redefinitions consistent with this fall-off 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 non-perturbative tools to explore them.