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

TL;DR

This paper extends the large D gravity and low D string theory correspondence to include T-dual solutions, demonstrating that their near-horizon and near-singularity geometries with $oldsymbol{ extalpha'}$ corrections can be described by the two-dimensional Hohm-Zwiebach action, enabling non-perturbative analysis.

Contribution

It generalizes the large D and low D string correspondence to T-dual solutions and introduces the Hohm-Zwiebach action for systematic $oldsymbol{ extalpha'}$-corrected geometry analysis.

Findings

Large D limit reduces black hole geometries to two-dimensional near-horizon structures.

T-dual solutions with naked singularities also reduce to two-dimensional geometries.

Hohm-Zwiebach action captures $oldsymbol{ extalpha'}$ corrections and allows non-perturbative solutions.

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.