ABSTRACT
Since the remarkable realization by J. Scherk and J. Schwarz [22] that string spectrum contains gravitons one is looking for the stringy approach to the quantum gravity. One feature of quantum gravity - strong fluctuations of space-time topology at Planck scales, advocated by S. Hawking [7], was very elusive. The reason is that the conventional approach to string quantization produces S-matrix in the form of the expansion in string coupling constant. The S-matrix describes, at best, the scattering of the gravitational waves in some stringy background, most commonly the Minkowski background (however recent advances in AdS/CFT duality allow to hope for other homogeneous spaces as well). At finite order of string perturbation theory one has a finite number of gravitons, so it is unlikely that the strong fluctuation of the space-time topology would be seen. The only hope is to resum the string perturbation theory, perhaps analytically continuing in the string coupling: https://www.w3.org/1998/Math/MathML"> e x p ∑ g = 0 ∞ g s 2 g − 2 F g ( a ) + O e − 1 g s = ∫ bndry cndts a D μν D ( … ) e x p − S e f f g μv , … , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq58.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
