Baryons and the deuteron as solitons: electric dipole moment and other properties from holographic QCD

We employ a holographic dual of a QCD-like theory, the model of Witten-Sakai-Sugimoto, to study general properties of the baryons and in particular to compute the contribution of the QCD θ angle to the electric dipole moment of the nucleons and of the deuteron bound state. This model uses a top-down approach, encoding color and flavor degrees of freedom in the gauge fields living on appropriately engineered stacks of D-Branes from type IIA string theory: the theory on flavor branes describes mesons as fundamental excitations of the fields, while baryons are realized as solitonic configurations. Such solitons in the low energy regime become Skyrmions, the first example of baryons as solitons. In the Skyrme model, a term that is sextic in derivatives of the pion field can be generated by integration of the ω vector mesons: we generalize this procedure in the holographic setup, extending it to the whole tower of mesons with the same quantum numbers. Using this result, we show how the ’t Hooft coupling λ can be seen as an interpolation parameter between two BPS configurations of the baryon. Implementing a finite (degenerate) quark mass term to the model promotes the holographic θ to a physical parameter as happens in QCD, and perturbations it generates in the baryon fields can be used to compute the electric dipole moment of such baryons. At leading order we previously obtained a purely isovector operator: now we move to next to leading order and find an isoscalar contribution that we use to compute the electric dipole moment of the deuteron. Then, turning on a quark mass difference, we discuss the arising of isospin breaking perturbations of the baryons and how these produce a splitting in the components of the moment of inertia of the solitonic baryon, and how this simple "symmetric top" model can account for mass splittings in isospin multiplets.