We present a detailed derivation of the two sum rules relating the spinpolarizabilities measured in real, virtual, and doubly-virtual Comptonscattering. For example, the polarizability $\delta_{LT}$, accessed ininclusive electron scattering, is related to the spin polarizability$\gamma_{E1E1}$ and the slope of generalized polarizabilities$P^{(M1,M1)1}-P^{(L1,L1)1}$, measured in, respectively, the real and thevirtual Compton scattering. We verify these sum rules in different variants ofchiral perturbation theory, discuss their empirical verification for theproton, and prospect their use in studies of the nucleon spin structure.
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