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

Abstract

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 $$ \mathcal{N} $$ N = 4 ungauged and gauged bosonic supergravity. In contrast to flat backgrounds, all the AdS4 results are found to be non-topological, providing a wider “infrared window” into the microscopic degrees of freedom of black holes in string theory.

Non-perturbative correction on the black hole geometry

“…As a black hole size is reduced due to the Hawking radiation, the thermal fluctuations become important and black hole entropy may corrected by a logarithmic term at leading order [3][4][5]. This logarithmic correction (perturbative correction) on the black hole entropy will modify the black hole thermodynamics so there are several works where mentioned perturbative correction have been investigated [6][7][8][9][10][11][12][13][14], which is also extended to other black objects like black rings [15]. These corrections may be used to test the quantum theory of gravity [16].…”