Self-dual supergravity in seven dimensions with reduced holonomy <f>G2</f>

We present self-dual <f>N=2</f> supergravity in superspace for Euclidean seven dimensions with the reduced holonomy <f>G2⊂SO(7)</f>, including all higher-order terms. As its foundation, we first establish <f>N=2</f> supergravity without self-duality in Euclidean seven dimensions. We next show how the generalized self-duality in terms of octonion structure constants can be consistently imposed on the superspace constraints. We found two self-dual <f>N=2</f> supergravity theories possible in 7D, depending on the representations of the two spinor charges of <f>N=2</f>. The first formulation has both of the two spinor charges in the <f>7</f> of <f>G2</f> with <f>24+24</f> on-shell degrees of freedom. The second formulation has both charges in the <f>1</f> of <f>G2</f> with <f>16+16</f> on-shell degrees of freedom. [Copyright &y& Elsevier]