Heterotic superstring vacua in four dimensions based on non-compact affine current algebras

• Published in: Nuclear physics. B 1990-04, Vol.334 (1), p.125-171
• Main Author: Bars, Itzhak
• Format: Article
• Language: English
• Subjects: Classical and quantum physics: mechanics and fields; Exact sciences and technology; Physics
• ISSN: 0550-3213; 1873-1562
• DOI: 10.1016/0550-3213(90)90659-2

New classes of unitary conformal and superconformal theories based on cosets of affine non-compact current algebras are suggested. Unitarity restrictions and the structure of the modules labelled by the primary states are discussed in general terms as well as in detail for SU(1,1)/ U(1), SU(N,M)/ SU(N) × SU(M) × U(1) and SL(2, C)/ SU(2) . Large classes of new N = 2 superconformal theories are classified and their central charges computed. This gives the non-compact counterpart of the Kazama-Suzuki models. It is shown that compact group and non-compact group Kazama-Suzuki models can be rewritten as coset models of the form (G × H)/H, where H is a maximal compact subgroup of G and G/H is kählerian. This reveals new symmetry structures which are useful in computations. It is shown that, in applications to heterotic superstring model building in four dimensions, a c ⩽ 9 compact space can be constructed only from two non-compact N = 2 super-affine cosets based on SU(1,1) − k ̂ with k ̂ ⩾ 3 and SU(2,1) − k ̂ with k ̂ ⩾ 9 . After performing a GSO projection and heterotic conversion à la Gepner, the massless spectrum of the c = 9 SU(1,1) −3 case is analysed in detail. With some simplifying assumptions on modular invariants it is outlined how the number of families would be computed.