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Hidden symmetries of the Nambu–Goto action
2006
Physics Letters B
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We organize the eight variables of the four-dimensional bosonic string (Ẋ^μ, X'^μ) into a 2 x 2 x 2 hypermatrix a_AA'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.
doi:10.1016/j.physletb.2006.08.050
fatcat:of5clgedy5efbgglqj44rfjsm4