Deep Inelastic Scattering and Gauge/String Duality

TL;DR

This paper analyzes deep inelastic scattering in gauge theories with holographic duals, revealing a qualitative transition from parton-like DIS at weak coupling to hadron-like scattering dominated by double-trace operators at strong coupling, with a continuous shift around gN~1. It develops both field-theoretic OPE analyses and string/gravity computations in AdS5×W to derive structure functions across three Bjorken x regimes: x~1 (supergravity states), x~(gN)^{-1/2} (excited strings), and x~e^{-(gN)^{1/2}} (string growth). The authors introduce a worldsheet renormalization group approach to sum logs and capture the nonlocal diffusion effects essential at exponentially small x, and they connect these results to Regge/Pomeron physics in the strong coupling limit. The work provides conceptual and technical insights into how hadronic substructure evolves with coupling in holographic theories and develops methods potentially applicable to QCD-like duals and beyond.

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.

Figures (10)

• Figure 1: Running coupling in the ${\cal N}=1^*$ theory. For the solid curve the asymptotic $\alpha N$ is large and the decoupling scale $m$ is close to $\Lambda$. For the dashed curve the asymptotic $\alpha N$ is small and the decoupling scale is $m' \gg\Lambda$. The asymptotically free ${\cal N}=1$ curve is dotted.
• Figure 2: Forward Compton amplitude in the parton model.
• Figure 3: Forward Compton amplitude with parton evolution; the parton splits, losing some fraction of its energy, before being struck by the photon.
• Figure 4: As $gN$ increases the splitting rate increases as well; a large fraction of the parton's energy is lost before it is struck.
• Figure 5: