String Theory and the Size of Hadrons

TL;DR

The paper addresses the long standing problem of off-shell currents and infinite hadron size in string theory. It proposes a holographic AdS/CFT framework in which four-dimensional hadrons are described as a superposition of fat strings from the five-dimensional bulk, with a Y dependent dressing that cures the divergences. Through a renormalization-group analysis in AdS, it shows that the would-be divergence in $\langle X^2 \rangle$ is tamed by $Y$ fluctuations and that the short-distance behavior flows to a fixed point corresponding to $X^2+Y^2$. A holographic calculation of form factors at large 't Hooft coupling reveals parton-like scaling controlled by the conformal dimension $\Delta$ and shows that the confinement scale $Y^*$ sets the hadron size, with the gauge theory tension related by holographic redshift as $\alpha'_{\\text{gauge}}^{1/2} \sim (gN)^{-1/4} Y^*$. The results agree with parton-model expectations in the appropriate limit.

Abstract

We begin by outlining the ancient puzzle of off shell currents and infinite size particles in a string theory of hadrons. We then consider the problem from the modern AdS/CFT perspective. We argue that although hadrons should be thought of as ideal thin strings from the 5-dimensional bulk point of view, the 4-dimensional strings are a superposition of "fat" strings of different thickness. We also find that the warped nature of the target geometry provides a mechanism for taming the infinite zero point fluctuations which apparently produce a divergent result for hadronic radii. Finally a calculation of the large momentum behavior of the form factor is given in the limit of strong 't Hooft parameter where the classical gravity limit is appropriate. We find agreement with parton model expectations.