Large $D$ gravity and low $D$ string via $\alpha^{\prime}$ corrections

Abstract

In this paper, we generalize the correspondence between large $D$ gravity and low $D$ string theory to the most general case, including its T-dual solutions. It is well-known that the large $D$ limit of the Schwarzschild-Tangherlini black hole in gravity becomes a two-dimensional near-horizon geometry. Similarly, the large $D$ limit of its T-dual solution, obtained by the Buscher rules, namely the string black hole with a naked singularity, reduces to a two-dimensional near-singularity geometry. Both of these geometries are described by the two-dimensional low-energy effective action of string theory and are related to each other by scale-factor duality. Secondly, we demonstrate that these near-horizon/singuglarity geometries, including complete $\alpha^{\prime}$ corrections, can be described by the two-dimensional Hohm-Zwiebach action. This approach allows for the derivation of non-perturbative and non-singular solutions. Furthermore, the Hohm-Zwiebach action provides a systematic way to investigate the $\alpha^{\prime}$-corrected near-horizon/singularity geometries of different kinds of black holes, which are difficult to achieve through the Wess-Zumino-Witten (WZW) model method.