Logarithmic correction to black hole entropy in universal low-energy string theory models

We calculate the logarithmic correction to the entropy of asymptotically flat and AdS black holes (rotating, non-rotating, charged, and uncharged) embedded in Einstein-Maxwell-dilaton (EMD) theories with $U(1)$-charged. The leading quantum gravitational corrections are achieved in both extremal and non-extremal limits of black hole temperature by designing a common Euclidean gravity setup that evaluates the “logarithmic term” from one-loop effective actions via heat kernel method-based calculations. EMD theories are universal building blocks of compactified string theory or supergravity models in 4D. For a concrete example, we generalize the entire setup and calculate logarithmic corrections for black holes in $U(1{)}^2$-charged EMD models intersecting with $\mathcal{N}=4$ ungauged and gauged bosonic supergravity. In contrast to flat backgrounds, all the AdS${}_4$ results are found to be non-topological, providing a wider “infrared window” into the microscopic degrees of freedom of black holes in string theory.