By Bailin, Love.
The compactification of the heterotic string concept on a six-dimensional orbifold is appealing theoretically, because it allows the entire choice of the emergent 4-dimensional powerful supergravity thought, together with the gauge workforce and topic content material, the superpotential and Kahler capability, in addition to the gauge kinetic functionality. This evaluate makes an attempt to survey all of those calculations, overlaying 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 selection of the non-perturbative powerful power for the moduli bobbing up from hidden quarter gaugino condensation, and its reference to supersymmetry breaking. We finish with a quick dialogue of the relevance of weakly coupled string idea within the gentle of contemporary advancements at the strongly coupled concept.
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Extra resources for Orbifold compactifications of string theory
Example text
Unlike the usual discrete Wilson lines, continuous Wilson lines are able to reduce the rank of the gauge group. The gauge "elds associated with the Cartan subalgebra are of the form bG "02 ' "02 , I"1,2,16, where i is a four dimensional space-time index. While acts trivally \ 0 \ * on bG , has a non-trivial action on some of the left-mover bosonic oscillators ' . As \ \ a consequence of point group invariance, some of the gauge "elds of the Cartan subalgebra are projected out of the theory, leaving only that part of the Cartan subalgebra for while ' is \ unrotated by .
This prevents us pulling out the ( K, L) factor from the summation to leave a simple GSO projection. Instead, it is necessary to evaluate the degeneracy factor in the partition function. 57) D( K)" N L and states for which D( K) is zero are projected out. In the presence of Wilson lines, Eq. 58) 322 D. Bailin, A. (P#m<#r "(mn/2)v( #n . 59) In Eq. 59), the space group elements associated with "xed points in the K and L twisted sectors have been written as ( K,r e #(1! K) ) and ( L,r e #(1! L) ).
Although by sifting through consistent orbifold compacti"cations we can "nd a range of possibilities for the massless spectrum, this range is not in general wide enough to permit the presence of adjoint or larger representations, as we now discuss. The largest representations of the gauge group that can occur in a string theory are controlled by the level of the Kac}Moody algebra [111] (or current algebra) for the left movers, which is de"ned as follows. The vertex operator