Hidden symmetries of the Nambu-Goto action
Abstract
Description
We organize the eight variables of the four-dimensional bosonic string ({\dot X}^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 \sqrt{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.
Version appearing in Phys. Lett. B . 5 pages latex
Version appearing in Phys. Lett. B . 5 pages latex