Gauss-Bonnet corrected string/black hole transition in large dimensions

We develop a unified analytic treatment of the Horowitz–Polchinski string/black hole correspondence that systematically incorporates higher-derivative corrections to gravity. Working in Euclidean signature – where the Euclidean black hole and the thermal scalar arise as competing saddles of the same finite-temperature ensemble – we include the Gauss–Bonnet term. The analysis is rendered tractable in this UV–sensitive regime by the large-$D$ expansion, which sharply separates the geometry into a universal near-zone and an asymptotic far-zone. In the near-zone, the coupled large-$D$ equations reduce the thermal-scalar sector to an exactly solvable Schrödinger problem, from which we extract the ${\alpha }^{\mathrm{\prime }}$-corrected decay exponent and the corresponding shift of the Hagedorn temperature. In the far-zone, we construct closed-form Euclidean solutions of Einstein–Gauss–Bonnet theory at leading order in both $1\mathrm{/}D$ and ${\alpha }^{\mathrm{\prime }}$. Matching the two regions yields the complete corrected saddle – fixing its temperature, horizon data, and on–shell action – and permits a fully analytic comparison of free energies between the thermal-scalar and black hole phases. This provides a controlled derivation of the HP correspondence point with explicit higher-curvature corrections.