Pion and kaon D terms from holographic QCD and coupled-channel dispersion relations

For a spin-zero meson, the exact trace identity relates the D term to the tensor gravitational form factor AM(t) and the total scalar trace ΘM(t). We study the pion and kaon D terms by combining a holographic tensor form factor with a chiral-dispersive representation of the trace. Its normalization and slope at the origin are obtained from the forward Ward identity and curved-space SU(3) chiral perturbation theory. A two-channel ππ/K K Muskhelishvili--Omnès solution constructed from empirical scattering amplitudes describes the continuation to spacelike momentum. Available lattice-QCD results are shown for comparison. In the chiral limit, saturation of the trace by the normalized explicit quark-mass response gives D_π(0)=-1/3, while the soft-pion theorem gives D_π(0)=-1. This comparison separates the explicit-mass contribution from the remaining chiral scalar response. At physical masses, SU(3) breaking in the chiral matching distinguishes the pion and kaon forward values, and coupled-channel rescattering governs their evolution away from the origin. The kaon D term is less negative than the pion result in the low-Q² spacelike region considered, with the separation decreasing as Q² increases. These form factors provide a low-energy reference for future lattice studies of the tensor and scalar channels.