Green-Schwarz, Nambu-Goto Actions, and Cayley's Hyperdeterminant

Details Green-Schwarz, Nambu-Goto Actions, and Cayley's Hyperdeterminant Green-Schwarz, Nambu-Goto Actions, and Cayley's Hyperdeterminant

2007-09-07

arxiv.org/abs/0709.0973v1

Phys.Lett.B652:135-140,2007

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, no figures

Scientific paper

10.1016/j.physletb.2007.06.063

It has been recently shown that Nambu-Goto action can be re-expressed in terms of Cayley's hyperdeterminant with the manifest SL(2,R) X SL(2,R) X SL(2,R) symmetry. In the present paper, we show that the same feature is shared by Green-Schwarz sigma-model for N=2 superstring whose target space-time is D=2+2. When its zweibein field is eliminated from the action, it contains the Nambu-Goto action which is nothing but the square root of Cayley's hyperdeterminant of the pull-back in superspace \sqrt{\hyperdet(\Pi_{i \a\Dot\a})} manifestly invariant under SL(2,R) X SL(2,R) X SL(2,R). The target space-time D=2+2 can accommodate self-dual supersymmetric Yang-Mills theory. Our action has also fermionic kappa-symmetry, satisfying the criterion for its light-cone equivalence to Neveu-Schwarz-Ramond formulation for N=2 superstring.

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