Beyond Supergravity in AdS-CFT: An Application to Jet Quenching

Abstract

These notes are dedicated to the study of jet quenching in the strongly coupled limit using gauge/string duality. We are interested in corrections to the infinite coupling λ = ∞ result for the jet stopping, in powers of λ −1∕2. To estimate these corrections we need to go beyond supergravity in AdS-CFT, and include all higher-derivative corrections to the supergravity action which arise from the string α′ expansion. For the particular type of “jets” that we study, the expansion in λ −1∕2 is well behaved for jets whose stopping distance l stop is in the range \(\lambda ^{-1/6}\ell_{\mathrm{max}} \ll \ell_{\mathrm{stop}} \lesssim \ell_{\mathrm{max}}\), but the expansion breaks down for jets created in such a way that \(\ell_{\mathrm{stop}} \ll \lambda ^{-1/6}\ell_{\mathrm{max}}\). The reason for the breakdown of the λ −1∕2 expansion is caused by the excitation of massive string states. In particular, consider “jets” which are dual to high-momentum gravitons. In the black brane background the gravitons, which are closed string states, get stretched into relatively large classical strings by tidal forces. These stringy excitations of the graviton are not contained in the supergravity approximation, but the jet stopping problem can nonetheless still be solved by drawing on various string-theory methods (the eikonal approximation, the Penrose limit, string quantization in pp-wave backgrounds) to obtain a probability distribution for the late-time classical string loops.