Supersymmetric R2 actions, conformal invariance and the Lorentz Chern-Simons term in 6 and 10 dimensions

Abstract

We consider the superconformal extension of R 2 actions in 6 and 10 dimensions. We show that the fields of the conformal multiplet alone admit a one parameter family of R 2 actions of the form φ[ R μνab 2 + α( R μνab 2 − 4 R μa 2 + R 2)]. In d=6 we give the supersymmetric action for α=0, while for α≠0 we give partial results. We show that for α=0 and in a conformal gauge the 3-form field H μνϱ has a natural torsion interpretation. In d=10 we find similar results (except the torsion interpretation) up to variations containing the 7-form field strength.