Green–Schwarz, Nambu–Goto actions, and Cayley's hyperdeterminant

2007/07/02 by Hitoshi Nishino, Subhash Rajpoot · 6 citations
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Algebra and Geometry #Black Holes and Theoretical Physics #Computer science #Geometry #Goto #Homogeneous space #Invariant (physics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Superspace #Superstring theory #Supersymmetry #hep-th

paper · pdf · doi:10.1016/j.physletb.2007.06.063

published in Physics Letters B 652(2-3), 135-140 (Elsevier BV) · 14 pages, no figures

openalex publication_date 2007/07/02 · arxiv created 2007/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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)×SL(2,R)×SL(2,R) symmetry. In the present Letter, we show that the same feature is shared by Green–Schwarz σ-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 Det(Πiαα˙) manifestly invariant under SL(2,R)×SL(2,R)×SL(2,R). The target space–time D=2+2 can accommodate self-dual supersymmetric Yang–Mills theory. Our action has also fermionic κ-symmetry, satisfying the criterion for its light-cone equivalence to Neveu–Schwarz–Ramond formulation for N=2 superstring.

Citations

• The Self-Duality Equations on a Riemann Surface
• THE INVARIANT CHARGES OF THE NAMBU–GOTO STRING THEORY: QUANTIZATION OF NON-ADDITIVE COMPOSITION LAWS
• String triality, black hole entropy, and Cayley’s hyperdeterminant
• Some Exact Multipseudoparticle Solutions of Classical Yang-Mills Theory
• Quantum geometry of bosonic strings
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• N=2 (4) string theory is self-dualN=4 Yang-Mills theory
• N=4 string is the same as theN=2 string
• Strings, black holes, and quantum information
• A cubic action for self-dual Yang-Mills
• Distributed Entanglement