Ramond–Neveu–Schwarz model

introduction

In January 1971 Pierre Ramond constructed A dual model with fermions
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.

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.

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

[{'LOWER': 'rns'}, {'LEMMA': 'formalism'}]
[{'LOWER': 'ramond'}, {'OP': '*'}, {'LOWER': 'neveu'}, {'OP': '*'}, {'LOWER': 'schwarz'}, {'LEMMA': 'formalism'}]