Scattering length in holographic confining theories

The low-energy effective theory description of a confining theory, such as QCD, is constructed, including local interactions between hadrons organized in a derivative expansion. This kind of approach also applies more generically to theories with a mass gap, once the relevant low-energy degrees of freedom are identified. The strength of local interactions in the effective theory is determined by the low-momentum expansion of scattering amplitudes, with the scattering length capturing the leading order. We compute the main contribution to the scattering length between two spin-zero particles in strongly coupled theories using the gauge/gravity duality. We study two different theories with a mass gap: a massive deformation of N = 4 super-Yang-Mills theory (N = 1 ∗) and a nonsupersymmetric five-dimensional theory compactified on a circle. These cases have a different realization of the mass gap in the dual gravity description: the former is the well-known GPPZ singular solution and the latter a smooth AdS6 soliton geometry. We find that the scattering lengths have similar functional dependences on the masses of the particles and on the conformal dimension of the operators that create them in both theories. Assuming these similarities hold more generally, they could be used to constrain the effective description of gapped strongly coupled theories beyond symmetry considerations.