Ramond–Neveu–Schwarz model

introduction

• The Dual Resonance Model is generalized to spacetime fermions by Ramond
• an extension of the Dual Resonance Model for pions is constructed by Neveu and Schwarz
• 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

• These efforts extended from the independent attempts of Lovelace and Shapiro to obtain the amplitude for the scattering of four pions to the construction of dual models for the scattering of particles with internal symmetry and with spin.
• The first dual model including fermions was obtained by Ramond, as well as the immediately following model proposed by Neveu and Schwarz for extending the Lovelace–Shapiro amplitude to an arbitrary number of pions.
• 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