Neutron-proton mass difference from gauge/gravity duality

Understand

Using gauge/gravity duality as a tool, we compute the strong sector, isospin breaking induced contribution to the neutron-proton mass difference in the Witten-Sakai-Sugimoto model of large $N$ QCD with two non-degenerate light flavors.

• The mass difference, for which we provide an analytic expression, turns out to be positive and proportional to the down-up quark mass splitting, consistently with expectations and previous estimates based on effective QCD models.
• Extrapolating the model parameters to fit QCD hadronic observables, we find that the strong sector contribution to the nucleon mass splitting overcomes the electromagnetic contribution and is about $0.25\%$ of the average nucleon mass in the model, a result which approaches recent lattice QCD estimates.
• Our formula is extended to resonances and $\Delta$ baryons.