Volume 142, number 1,2 PHYSICS LETTERS 12 July 1984 A SUPERUNIHCATION MODEL OF EMBEDDING N = 1 SUSY GUT INTO N = 8 ESG ZHANG De-Hal Physics Department, Peking University, Bei]ing, People's Republic of China and WU Zu-Yu Department Two, Beifinglnstitute of Technology, Belling, People's RePublic of China Received 19 Januazy 1984 SU(8) Starting from the composite supermultiplet (2, 28}~Y= 8 ofN = 8 ESG and using Veltman's conjecture applied in re- normalizable N = 1 SUSY Yang-Mills theory, we obtained the particle contents of the SUSY SU(5) GUT with just 3 gene- rations of leptons and quarks to which the new quantum numbers of localized R-symmetry were given. Recently, interest in supersymmetric grand unification theory (SUSY GUT) [1] has been increasing over the conventional minimal SU(5) GUT [2] which suffers difficulties of fast proton decay and the hierarchy problem. The lagrangian of SUSY GUT coupling with N = 1 supergravity can be written as [3] .re = f a 4 o E{ ¢(S, Se 2v) + Re {R-1 [g(S) + fa#(S)Wa ~ eabWflb] }}. (1) If one can determine (1) what group the internal symmetry of SUSY GUT is, (2) what representation contents the chiral supermultiplets S are, and (3) what formulas and parameters the potentials ¢(S, S),g(S) and f~¢(S) have, then the whole theory of SUSY GUT is fixed completely. On the other hand, it is suspected that N = 8 extended supergravity (ESG) [4] may be a finite theory, in spite of its unrenormalizability, which can umfy the electroweak, color and gravitational interactions. Ellis, Galliard, " 3 - SU(8) Maiani and Zumino (EGMZ) first constructed a superunification model [5] in which they took (g, 8}N=8 as the composite supermultiplet and obtained the conventional SU(5) GUT with just 3 generations of particles, if the as- sumption of discarding the trace is taken, The aim of the present article is to obtain a SUSY GUT from N = 8 ESG. Indeed, we got that the group of SUSY GUT is SU(5) and determined the contents of chiral supermultiplets of the theory which contained just 3 generations of quarks and leptons. SO(8) The fundamental supermultiplet ofN = 8 ESG is{2, 1}~r~ 8 ,which is too small to assign all particles known in the standard model of the electroweak and strong interactions [6]. Cremmer and Julia discovered that N --- 8 ESG has a global E 7 ® local SU(8) hidden symmetry and conjectured that the composite gauge fields of local SU(8) can become dynamical gauge bosons at the quantum level [3]. EGMZ further suggested that all the composite fields should form a complete N = 8 supermultiplet rather than only (1,63) sU(8) states. We think that it is reasonable to assume that the composite supermultiplet does not contain any states with he- licity larger than 2 which do not have a consistent interaction field theory. Under this restriction, the composite .... 8~sU(8) which content is given in the table 1 [7]. supermultiplet with a minimal number ofhelicity states lSlZ, z ~N=8 It is easy to see from its scalar contents that if the 28-plet of SU(8) acquires a non-zero vacuum expectation value (VEV), then the internal symmetry SU(8) associated withN = 8 supersymmetry will be broken as 35