Baryon Spectra and AdS/CFT Correspondence

TL;DR

This work establishes a precise link between wrapped D-branes on cycles within AdS backgrounds and dibaryon operators in the dual CFT, showing that a U(1)_R gauge field from Kaluza–Klein reduction mediates R-charge and that operator dimensions correlate with wrapped-brane volumes. By analyzing both $AdS_5\times T^{1,1}$ and $AdS_4\times X_7$ geometries, the authors derive exact relations between R-charge and conformal dimension, with $\Delta$ set by cycle volumes and reproducing $\Delta=3N/4$ and $Q_R=N/2$ for the conifold-like case, as well as providing a framework for collective-coordinate quantization and BPS open-string excitations. They develop a moduli-space quantization picture in which ground-state counting of dibaryons matches holomorphic sections of line bundles over $\mathbb{C}P^m$, and they compute the spectrum of BPS fluctuations of wrapped D3-branes, finding spectra that align with chiral primaries and their conformal-weight shifts. Overall, the results reinforce the necessity of stringy objects (D-branes) in the AdS/CFT state/operator map at large $N$ and offer a concrete approach to open-string sectors and giant-graviton phenomena in quiver gauge theories.

Abstract

We provide a detailed map between wrapped D3-branes in Anti-de Sitter (AdS) backgrounds and dibaryon operators in the corresponding conformal field theory (CFT). The effective five dimensional action governing the dynamics of AdS space contains a $U(1)_R$ gauge field that mediates interactions between objects possessing R-charge. We show that the $U(1)_R$ charge of these wrapped D3-branes as measured by the gauge field matches the R-charge of the dibaryons expected from field theory considerations. We are able, through a careful probe brane calculation in an $AdS_5\times T^{1,1}$ background, to understand the exact relation between the mass of the wrapped D3-brane and the dimension of the corresponding dibaryon. We also make some steps toward matching the counting of dibaryon operators in the CFT with the ground states of a supersymmetric quantum mechanical system whose target space is the moduli space of D-branes. Finally, we discuss BPS excitations of the D3-brane and compare them with higher dimension operators in the CFT.