The local logarithmic conformal field theory corresponding to the triplet a
lgebra at c = -2 is constructed. The constraints of locality and duality ar
e explored in detail, and a consistent set of amplitudes is found. The spec
trum of the corresponding theory is determined, and it is found to be modul
ar invariant. This provides the first construction of a non-chiral rational
logarithmic conformal field theory, establishing that such models can inde
ed define bona fide conformal field theories. (C) 1999 Elsevier Science B.V
.