Extremal black string with Kalb-Ramond field via $\alpha^{\prime}$ corrections

TL;DR

This paper presents a novel method to derive a non-perturbative, non-singular extremal black string solution with a Kalb-Ramond field, incorporating complete $ extalpha'$ corrections, advancing understanding of complex string theory solutions.

Contribution

Introduces a new technique transforming infinite matrix differential equations into trace calculations, enabling the derivation of regular extremal black string solutions with $ extalpha'$ corrections and Kalb-Ramond fields.

Findings

Derived a regular extremal black string solution with $ extalpha'$ corrections.

Developed a method simplifying matrix differential equations into trace form.

Provided a framework for studying complex non-perturbative solutions in string theory.

Abstract

In this paper, we obtain the three-dimensional regular extremal black string solution incorporating $\alpha'$ corrections and a non-trivial Kalb-Ramond field. The difficulty in considering the Kalb-Ramond field lies in the fact that it transforms the original equations of motion into an infinite summation form involving matrices, making it difficult to calculate the matrix differential equations. To solve this problem, we introduce a new method that transforms the infinite summation of matrix differential equations into a simple trace of the matrix. As a result, we are able to obtain a non-perturbative and non-singular extremal black string solution. Indeed, this work serves as a good example for studying more complicated non-perturbative solutions that incorporate the Kalb-Ramond field via complete $\alpha'$ corrections.