Electromagnetic form factors from the fifth dimension

TL;DR

This paper uses holographic duality to compute electromagnetic form factors of mesons in a strongly coupled conformal field theory, revealing insights into meson structure and transitions at high momentum transfer.

Contribution

It introduces a method to calculate meson form factors at strong coupling using D7-brane fluctuations in AdS/CFT, extending understanding of meson structure in holographic models.

Findings

Form factors match parton model predictions at high momentum transfer.

Computed $ ext{γπρ}$ and $ ext{γ}f_0 ho$ transition form factors.

Analysis of the $ ext{γ}^* ext{γ}^* ext{π}$ form factor shows subtle differences from QCD.

Abstract

We analyse various $U(1)_{EM}$ form factors of mesons at strong coupling in an $\mathcal{N}=2$ flavored version of $\mathcal{N}=4$ $SYM$ which becomes conformal in the UV. The quark mass breaks the conformal symmetry in the IR and generates a mass gap. In the appropriate limit, the gravity dual is described in terms of probe $D7$-branes in $AdS_5\times S^5$. By studying the $D7$ fluctuations we find the suitable terms in a "meson effective theory" which allow us to compute the desired form factors, namely the $\gamma\pi\rho$ and $\gamma f_0\rho$ transition form factors. At large $q^2$ we find perfect agreement with the naive parton model counting, which is a consequence of the conformal nature of both QCD and our model in the UV. By using the same tools, we can compute the $\gamma^*\gamma^*\pi$ form factor. However this channel is more subtle and comparisons to the QCD result are more involved.