Neutron-proton mass difference from gauge/gravity duality

Using gauge/gravity duality as a tool, we compute the strong sector 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 turns out to be a $1/N$ effect, to be positive and proportional to the down-up quark mass splitting, consistently with expectations and previous estimates based on effective QCD models. Our result is analytically expressed in terms of the few parameters of the model and it accounts for the contribution of the whole (axial) vector meson tower. Extrapolating the parameters to fit QCD mesonic 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 easily extended to generic baryons (and the corresponding excited states) with only up and down constituent quarks. We use it to also compute the strong sector contribution to $\Delta$ baryons mass differences. Finally, we also provide details of how isospin breaking affects the holographic instanton solution describing the baryons.