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By Bailin, Love.

The compactification of the heterotic string conception on a six-dimensional orbifold is appealing theoretically, because it allows the entire selection of the emergent 4-dimensional powerful supergravity conception, together with the gauge staff and topic content material, the superpotential and Kahler capability, in addition to the gauge kinetic functionality. This evaluation makes an attempt to survey all of those calculations, protecting the development of orbifolds which yield (four-dimensional space-time) supersymmetry; orbifold version development, together with Wilson strains, and the modular symmetries linked to orbifold compactifications; the calculation of the Yukawa couplings, and their reference to quark and lepton plenty and combining; the calculation of the Kahler capability and its string loop threshold corrections; and the decision of the non-perturbative powerful capability for the moduli coming up from hidden area gaugino condensation, and its reference to supersymmetry breaking. We finish with a short dialogue of the relevance of weakly coupled string thought within the gentle of contemporary advancements at the strongly coupled idea.

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21) 332 D. Bailin, A. Love / Physics Reports 315 (1999) 285}408 If we consider a coupling of three states, each in the twisted sector, associated with "xed points f ,  f and f characterised by integers p, p and p, "1,3,5, respectively, then the point group   M M M selection rule is trivially satis"ed and the space group selection rule gives  p("0 mod 3, M "1,3,5 . 22) ( For non-prime order orbifolds [124,142,100,53], the discussion is a little more complicated. In this case, as we saw earlier, the "xed points of K are not necessarily the same as those of L, for mOn, and when constructing physical states we have to take linear combinations of "xed points to get an eigenstate of .

Bailin, A. 79) M MN N where is an E ;E lattice vector, re#ecting the fact that these are inequivalent paths on the torus   that are equivalent on the orbifold. One approach [48] to writing down all possible models is to list all possible choices of a(,J3E , M  and then to use the modular invariance conditions on a to limit the possible choices of a), K3E , M M  consistent with the choice of a(. There are various other transformations on the Wilson lines, and M the <' and Wilson lines together, that give equivalent models.

For a Z ;Z orbifold, generated by point group elements and , for the I l twisted sector, + , nv G must be replaced by kv G#l  G where v G and  G are the twists for and , respectively. Also n<'#r a' must be replaced by k<'#l='#r a' , where <' and =' are the embeddings in the M M M M gauge group of and . Naive space group invariance can not be applied in the twisted sectors, and the surviving states are those allowed by the generalised GSO projections [18,124,171]. In the case of the prime order orbifolds (Z and Z ) all twisted sector massless states survive these GSO projections, for arbitrary   embeddings of the point group and arbitrary Wilson lines [18,124].

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