Green-Schwarz, Nambu-Goto Actions, and Cayley's Hyperdeterminant
arXiv:0709.0973 · doi:10.1016/j.physletb.2007.06.063
Abstract
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(Π_{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.
14 pages, no figures
References in corpus (18)
- Distributed Entanglement
- Four Dimensional String/String/String Triality
- String triality, black hole entropy and Cayley's hyperdeterminant
- The N=2(4) string is self-dual N=4 Yang-Mills
- Strings, Black Holes, and Quantum Information
- Self-Dual N=8 Supergravity as Closed N=2(4) Strings
- A cubic action for self-dual Yang-Mills
- Self-Dual Supersymmetry and Supergravity in Atiyah-Ward Space-Time
- The N=4 string is the same as the N=2 string
- Majorana-Weyl Spinors and Self-Duality Gauge Fields in 2+2 Dimensions
- The LQG -- String: Loop Quantum Gravity Quantization of String Theory I. Flat Target Space
- Extended Supersymmetry and Self-Duality in 2+2 Dimensions
- Green-Schwarz Formulation of Self-Dual Superstring
- Supersymmetric Self-Dual Yang-Mills and Supergravity as Background of Green-Schwarz Superstring
- Hidden symmetries of the Nambu-Goto action
- Self--Dual Supergravity and Supersymmetric Yang--Mills Coupled to Green--Schwarz Superstring
- The Invariant Charges of the Nambu-Goto String Theory: Quantization of Non-Additive Composition Laws
- The invariant charges of the Nambu-Goto String and Canonical Quantization