GROUP-THEORETICAL STRUCTURE OF N = 1 AND N = 2 TWO-FORM SUPERGRAVITY

Abstract

We clarify the group-theoretical structure of N = 1 and N = 2 two-form supergravity, which is classically equivalent to the Einstein supergravity. N = 1 and N = 2 two-form supergravity theories can be formulated as gauge theories. By introducing two Grassmann variables θA (A = 1, 2), we construct the explicit representations of the generators Qi of the gauge group, which makes it possible to express any product of the generators as a linear combination of the generators [Formula: see text]. By using the expression and the tensor product representation, we show how to construct finite-dimensional representations of the gauge groups. Based on these representations, we construct the Lagrangians of N = 1 and N = 2 two-form supergravity theories.