Dual string models with non-Abelian colour and flavour symmetries

Some reminiscences from a long friendship

“…In this process we discovered with altogether a full football team of Italians that we could generalize this procedure to infinitely many super-Virasoro algebras [13] out of which two could be represented as extensions of the original ones. In this way we found two new supersymmetric string models [14,15], but none of them turned out to be close to the one we were searching for, a four-dimensional model with a hadronic spectrum. We were still looking for a model for the strong interactions.…”

A non-linear representation of the d=2 so (4)-extended superconformal algebra

“…In principle the field ~0 in the multiplet (~o,X') can be interpreted as a string-coordinate. However, due to the non-linearity of the supersymmetry transformations the formulation of "so(3)-or so(4)-strings" is not a straightforward extension of the results for strings with u(1)-or su(2)-extended supersyrfimetry [ 23,10,24 ].…”

“…2--W and the Wick theorem it is easily shown that the currents (10) satisfy the following short distance operator product expansions (OPE) with c= 3/2:…”

“…(ii) An exceptional N=4 SCA with the su(2) KMA as a subalgebra [9,10]. The SCA's exist in different varieties which are in general not equivalent (Neveu-Schwarz, Ramond, twisted, non-twisted, see e.g.…”

From N=2 strings to M-Theory

“…8 It does not, however, mean that the critical N=4 strings are 'the same' as the critical N=2 strings. 9 The idea of the string world-sheet complexification also appeared in the stidies of high-energy behavior of string theories [21]. It was first noticed by Siegel [7] that the self-duality and 'Lorentz' invariance in 2 + 2 dimensions imply the maximal supersymmetry.…”