Negative Corrections to Black Hole Entropy from String Theory

We report for the first time that in heterotic string compactified on 4-torus or equivalently IIA string compactified on K3, the leading ${\alpha }^{\mathrm{\prime }}$ corrections to the rotating black string entropy at fixed conserved charges can be negative. This further implies that the correction to the mass of extremal rotating string is positive, opposite to the standard expectation from the weak gravity conjecture. Our result suggests that the validity of positivity of entropy shift due to higher order operators depends on other factors omitted previously in the effective field theory analysis.