Ramond–Neveu–Schwarz model

introduction

• In January 1971 Pierre Ramond constructed a Dual Resonance Model generalization of the Dirac equation
• Neveu and Schwarz proposed a new bosonic dual model, which we called the ‘dual pion model’, in March 1971
• The two models are recognized as the two sectors of the Ramond–Neveu–Schwarz model
• In the Ramond–Neveu–Schwarz (RNS) model one introduces, besides the bosonic oscillators $\alpha_n$, the fermionic oscillators $\psi_r^{\mu}$, where $r$ is integer and half-integer in the Ramond (R) and Neveu–Schwarz (NS) sectors, respectively.
• This theory had a rich spectrum of states, including both bosons and fermions, and required $d = 10$ spacetime dimensions.

background

• Lovelace and Shapiro : the scattering amplitude of four pions to the construction of dual models
• Neveu and Schwarz : extending the Lovelace–Shapiro amplitude to an arbitrary number of pions, that is, for the scattering of particles with internal symmetry and with spin.
• The Ramond and Neveu–Schwarz models were soon recognized as the two sectors, fermionic and bosonic, of the same model, called the Ramond–Neveu–Schwarz (RNS) model.
• The spectrum contains both fermions and bosons, and is much richer than that of the dual resonance model. Unfortunately, it still contains a tachyon.

supersymmetry

• It was soon recognized, first by Gervais and Sakita, that the RNS model had a new kind of symmetry relating bosons and fermions. This was the first occurrence of supersymmetry.
• There is an equal number of bosons and fermions at every mass level. This was compelling evidence (though not a proof) for ‘ten-dimensional spacetime supersymmetry’ of the GSO-projected theory.
• The realization that it could have spacetime supersymmetry was a major advance.
• Wess and Zumino extend the world-sheet supersymmetry of the Ramond–Neveu–Schwarz model to four-dimensional field theory

related items

• GSO projection