  We present two alternative field contents for Bagger-Lambert theory, based on
the triality of SO(8). The first content is (\varphi_{A a}, \chi_{\dot A a} ;
A_\m{}^{a b}), where the bosonic field \varphi is in the 8_S of SO(8) instead
of the 8_V as in the original Bagger-Lambert formulation. The second field
content is (\varphi_{\dot A a}, \chi^I{}_a ; A_\m{}^{a b}), where the bosonic
field \varphi and the fermionic field \chi are respectively in the 8_C and 8_V
of SO(8). In both of these field contents, the bosonic potentials are positive
definite, as desired. Moreover, these bosonic potentials can be unified by the
triality of SO(8). To this end, we see a special constant matrix as a product
of two SO(8) generators playing an important role, relating the 8_V, 8_S and
8_C of SO(8) for the triality. As an important application, we give the
supersymmetry transformation rule for N=6 superconformal Chern-Simons theory
with the supersymmetry parameter in the 6 of SO(6), obtained by the truncation
of our first field content.
