High Energy Scattering in the AdS/CFT Correspondence

TL;DR

<3-5 sentence high-level summary> The thesis presents a comprehensive formulation of high-energy scattering in AdS/CFT by extending the eikonal approximation to AdS and interpreting the resulting amplitudes through conformal partial waves in the dual CFT. It shows that ladder and cross-ladder Witten diagrams with spin-$j$ exchanges resum into a generalized phase shift, which directly determines the small-$z, Lorentzian behavior of the CFT four-point function and the anomalous dimensions of high-spin double-trace operators. In particular, gravitational (graviton) exchanges dominate at large energy and impact parameter, yielding universal predictions for CFTs with AdS gravity duals via $2\\Gamma(E,J) \propto - (E-J)^4/(E J)$ at large $E\sim J$. The work thus provides a concrete quantitative bridge between bulk eikonal physics and boundary CFT data, including the CPW decomposition and the impact-parameter representation of conformal partial waves. The results have broad implications for understanding information propagation, causality, and universality in strongly coupled holographic theories.

Abstract

This work explores the celebrated AdS/CFT correspondence in the regime of high energy scattering in Anti--de Sitter (AdS) spacetime. In particular, we develop the eikonal approximation to high energy scattering in AdS and explore its consequences for the dual Conformal Field Theory (CFT). Using position space Feynman rules, we rederive the eikonal approximation for high energy scattering in flat space. Following this intuitive position space perspective, we then generalize the eikonal approximation for high energy scattering in AdS and other spacetimes. Remarkably, we are able to resum, in terms of a generalized phase shift, ladder and cross ladder Witten diagrams associated to the exchange of an AdS spin j field, to all orders in the coupling constant. By the AdS/CFT correspondence, the eikonal amplitude in AdS is related to the four point function of CFT primary operators in the regime of large 't Hooft coupling, including all terms of the 1/N expansion. We then show that the eikonal amplitude determines the behavior of the CFT four point function for small values of the cross ratios in a Lorentzian regime and that this controls its high spin and dimension conformal partial wave decomposition. These results allow us to determine the anomalous dimension of high spin and dimension double trace primary operators, by relating it to the AdS eikonal phase shift. Finally we find that, at large energies and large impact parameters in AdS, the gravitational interaction dominates all other interactions, as in flat space. Therefore, the anomalous dimension of double trace operators, associated to graviton exchange in AdS, yields a universal prediction for CFT's with AdS gravitational duals.

Figures (35)

• Figure 1: The flux lines of the chromoelectric field between quark and anti--quark.
• Figure 2: The Chew--Frautschi plot. Spin $J$ of the isospin $I=1$ even parity mesons against their mass squared. (From reference pomeronbook)
• Figure 3: Regge trajectory determined from the large energy (20--200 $GeV$) behavior of the differential cross section of the process $\pi^- + p \to \pi^0 + n$. The straight line is obtained by extrapolating the trajectory in figure \ref{['regge']}. (From reference pomeronbook)
• Figure 4: Total cross sections for elastic scattering at high energy. The cross sections rise slowly due to pomeron exchange. (From reference pomeronQCDbook)
• Figure 5: Integration contours in the complex $J$ plane.