View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server WIS/06/02–JAN–DPP January 24, 2002 Unitary minimal models of (3=2; 3=2; 2) superconformal algebraSW and manifolds of G2 holonomy Boris Noyvert e-mail:
[email protected] Department of Particle Physics, Weizmann Institute of Science, 76100, Rehovot, Israel. Abstract The (3=2; 3=2; 2) superconformal algebra is a algebra with two free parameters.SW It consists of 3 superconformal currentsW of spins 3=2, 3=2 and 2. The algebra is proved to be the symmetry algebra of the coset su(2) su(2) su(2) 1 ⊕su(2)⊕ . At the central charge c =102 the algebra coincides with the superconformal algebra associated to manifolds of G2 holonomy. The unitary minimal models of the (3=2; 3=2; 2) algebra and their fusion SW structure are found. The spectrum of unitary representations of the G2 holonomy algebra is obtained. Contents 1 Introduction 1 2 Structure of the (3=2; 3=2; 2) algebra 3 SW 3 Coset construction 4 3.1Preliminarydiscussion........................... 4 3.2Explicitconstruction............................ 5 4 N =1 superconformal subalgebras 7 5 Highest weight representations 10 5.1NSsector.................................. 11 5.2Ramondsector............................... 12 5.3Firsttwistedsector............................. 13 5.4Secondtwistedsector............................ 14 6 Minimal models 14 6.1Unitaryrepresentations........................... 14 6.2Fusionrules................................. 17 6.3Examples.................................. 19 6.3.1 c =3=2, λ =0model........................ 19 6.3.2 c =9=4, λ =0model........................ 19 7 Spectrum of the G2 conformal algebra 20 8 Summary 23 Appendix 24 A OPEs of the (3=2; 3=2; 2)algebra..................