Deep Inelastic Scattering and Gauge/String Duality

TL;DR

This paper explores deep inelastic scattering in gauge theories with string duals, revealing a transition from parton-like behavior to hadron-dominated scattering as the coupling strength increases, and analyzing different regimes of Bjorken x.

Contribution

It identifies a transition in dominant operators in the OPE and calculates structure functions across different regimes of coupling and Bjorken x in gauge/string duality.

Findings

At small gN, scattering is dominated by twist-two operators.

At large gN, double-trace operators dominate, representing entire hadrons.

Different x regimes correspond to supergravity states, excited strings, and string growth effects.

Abstract

We study deep inelastic scattering in gauge theories which have dual string descriptions. As a function of $gN$ we find a transition. For small $gN$, the dominant operators in the OPE are the usual ones, of approximate twist two, corresponding to scattering from weakly interacting partons. For large $gN$, double-trace operators dominate, corresponding to scattering from entire hadrons (either the original `valence' hadron or part of a hadron cloud.) At large $gN$ we calculate the structure functions. As a function of Bjorken $x$ there are three regimes: $x$ of order one, where the scattering produces only supergravity states; $x$ small, where excited strings are produced; and, $x$ exponentially small, where the excited strings are comparable in size to the AdS space. The last regime requires in principle a full string calculation in curved spacetime, but the effect of string growth can be simply obtained from the world-sheet renormalization group.