An algebraic construction of twin-like models

If the generalized dynamics of K field theories (i.e., field theories with a non-standard kinetic term) is taken into account, then the possibility of so-called twin-like models opens up, that is, of different field theories which share the same topological defect solution with the same energy density. These twin-like models were first introduced in Phys. Rev. D 82, 105006 (2010), Ref. [1], where the authors also considered possible cosmological implications and gave a geometric characterization of twin-like models. A further analysis of the twin-like models was accomplished in Phys. Rev. D 84, 045010 (2011), Ref. [2], with the help of the first order formalism, where also the case with gravitational self-interaction was considered. Here we show that by combining the geometric conditions of Ref. [1] with the first order formalism of Ref. [2], one may easily derive a purely algebraic method to explicitly calculate an infinite number of twin field theories for a given theory. We determine this algebraic construction for the cases of scalar field theories, supersymmetric scalar field theories, and self-gravitating scalar fields. Further, we give several examples for each of these cases.