Hidden symmetries of the Nambu-Goto action

Abstract We organize the eight variables of the four-dimensional bosonic string ( X ˙ μ , X ′ μ ) into a 2 × 2 × 2 hypermatrix a A A ′ A ″ and show that in signature ( 2 , 2 ) the Nambu–Goto Lagrangian is given by Det a where Det is Cayley's hyperdeterminant. This is invariant not only under [ SL ( 2 , R ) ] 3 but also under interchange of the indices A , A ′ and A ″ . This triality reveals hitherto hidden discrete symmetries of the Nambu–Goto action.