Quantum Gravity with Boundaries near Two Dimensions

TL;DR

This paper investigates quantum corrections to the Einstein-Hilbert action with boundaries near two dimensions, demonstrating renormalizability, computing geometric entropy beyond semiclassical limits, and linking it to string theory concepts.

Contribution

It introduces a renormalizable approach to quantum gravity with boundaries in near-two dimensions and connects geometric entropy to string susceptibility.

Findings

Einstein-Hilbert action with boundaries is renormalizable at one loop.

Geometric entropy is computed beyond semiclassical approximation.

Quantum corrections to black hole entropy can be renormalized via gravitational coupling.

Abstract

We evaluate the quantum corrections of the Einstein-Hilbert action with boundaries in the $2+\epsilon$ dimensional expansion approach. We find the Einstein-Hilbert action with boundaries to be renormalizable to the one loop order. We compute the geometric entropy beyond the semiclassical approximation. It is found that the exact geometric entropy is related to the string succeptibility by the analytic continuation in the central charge. Our results also show that we can renormalize the divergent quantum corrections for the Bekenstein-Hawking entropy of blackholes by the gravitational coupling constant renormalization beyond two dimensions.