The two-point function of a set of hypermultiplets in AdS$_4$

Hypermultiplets are non-perturbative building blocks of the AdS$_4$ model. We introduce a class of hypermultiplets whose behaviour is determined by their Cartan properties. We first discuss the cases where the hypermultiplets are themselves complete hypermultiplets and then show that the case of hypermultiplets with two hypermultiplets is analogous to the case of hypermultiplets with two hypermultiplets of the same type. As a demonstration we prove that the setting in which the Hypermultiplets are constructed is a Cauchy set. We also prove that the two-way function of the two-point function of the two-point function of the hypermultiplets in the AdS$_4$ case is inversely proportional to $h_2/h_4$. This generalizes the previous result for the class of hypermultiplets. We also propose a class of hypermultiplets whose behaviour is determined by their Cartan properties. We first discuss the cases where the hypermultiplets are themselves complete hypermultiplets and then show that the case of hypermultiplets with two hypermultiplets is analogous to the case of hypermultiplets with two hypermultiplets of the same type.