The paper by Andrew Strominger and Cumrun Vafa explores the microscopic origin of the Bekenstein-Hawking entropy for a class of five-dimensional extremal black holes in string theory. They derive the Bekenstein-Hawking area-entropy relation \( S_{BH} = A/4 \) by counting the degeneracy of BPS soliton bound states. The authors consider string theories with five noncompact dimensions and \( N = 4 \) supersymmetry, focusing on black holes that carry both axion charge \( Q_H \) and electric charge \( Q_F \). They find that extremal black holes with nonvanishing \( Q_F \) and \( Q_H \) preserve only \( 1/4 \) of the \( N = 4 \) supersymmetry and are bound states of minimally-charged BPS solitons. The leading degeneracy of these bound states is given by \( S_{stat} = 2\pi \sqrt{Q_H (\frac{1}{2} Q_F^2 + 1)} \), which agrees with the Bekenstein-Hawking entropy \( S_{BH} = 2\pi \sqrt{\frac{Q_H Q_F^2}{2}} \) for large charges. The paper also discusses the validity of string perturbation theory and its implications for the black hole information puzzle, suggesting that the results may provide new insights into this longstanding issue.The paper by Andrew Strominger and Cumrun Vafa explores the microscopic origin of the Bekenstein-Hawking entropy for a class of five-dimensional extremal black holes in string theory. They derive the Bekenstein-Hawking area-entropy relation \( S_{BH} = A/4 \) by counting the degeneracy of BPS soliton bound states. The authors consider string theories with five noncompact dimensions and \( N = 4 \) supersymmetry, focusing on black holes that carry both axion charge \( Q_H \) and electric charge \( Q_F \). They find that extremal black holes with nonvanishing \( Q_F \) and \( Q_H \) preserve only \( 1/4 \) of the \( N = 4 \) supersymmetry and are bound states of minimally-charged BPS solitons. The leading degeneracy of these bound states is given by \( S_{stat} = 2\pi \sqrt{Q_H (\frac{1}{2} Q_F^2 + 1)} \), which agrees with the Bekenstein-Hawking entropy \( S_{BH} = 2\pi \sqrt{\frac{Q_H Q_F^2}{2}} \) for large charges. The paper also discusses the validity of string perturbation theory and its implications for the black hole information puzzle, suggesting that the results may provide new insights into this longstanding issue.