$\alpha'$-corrections to Near Extremal Dyonic Strings and Weak Gravity Conjecture

We construct non-extremal dyonic string solutions in 6D minimal supergravity where the leading higher derivative corrections arise from either the type IIA string theory compactified on K3 or the heterotic string theory compactified on 4-torus. The thermodynamical quantities and Euclidean actions of the strings are computed. In the near extremal regime, we calculate the force felt by a probe fundamental string in the background of the macroscopic dyonic string with leading $\alpha'$ corrections. We find that in both the IIA and heterotic setups, away from extremality, the attractive force overwhelms the repulsive force. However, close to extremality, the $\alpha'$ corrections can reduce the attractive force in the isoentropic process, where the charges are fixed. This feature may be used as a new constraint for supergravity models with consistent quantum gravity embedding, in cases where the extremal limit coincides with the BPS limit and the higher derivative corrections do not affect the mass-to-charge ratio. By contrast, the $\alpha'$ corrections can enhance the attractive force in the isothermal or isoenergetic processes.