Classification of two-dimensional conformal supergravity theories with finite-dimensional algebras (original) (raw)

We present a list of all the finite supersyrnmetric extensions of the two-dimensional (2D) conformal algebra SO(2,2), which could lead to 2D superconformal gravity theories. The on-shell matter multiplets of the algebras allowing canonical spin-0 and-2 matter are constructed. Using these multiplets the Weyl and Yang-Mills anomalies are calculated. There are many new models. One new model is free of both Yang-Mills and Weyl anomalies, SU(1,1) X SU(2~1, 1), but only the algebras SU(1, 1)', OSP(1~2}, OSP(2~2}, SU(l, l)XOSP(1~2}, OSP(1~2}XOSP(2~2}, and SU(1,1) XOSP(2~2} lead to models free of all anomalies. These models correspond to the known string models.