Orbifold compactifications of string theory by Bailin, Love.

By Bailin, Love.

The compactification of the heterotic string idea on a six-dimensional orbifold is appealing theoretically, because it allows the complete selection of the emergent 4-dimensional powerful supergravity concept, together with the gauge team and subject content material, the superpotential and Kahler strength, in addition to the gauge kinetic functionality. This evaluate makes an attempt to survey all of those calculations, protecting the development of orbifolds which yield (four-dimensional space-time) supersymmetry; orbifold version construction, together with Wilson traces, 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 potent strength for the moduli coming up from hidden region gaugino condensation, and its reference to supersymmetry breaking. We finish with a short dialogue of the relevance of weakly coupled string concept within the gentle of modern advancements at the strongly coupled conception.

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For the Z orbifold, with f of the form given in Eq. 20), v takes the form   v" d (e #e )#(I! p H\ H\ H\ and the integers p( , J"1,2, take the values H\ p( "0,$1 . 67) D. Bailin, A. 68) H\ H\ H H\ H\ H\ H H H with k and k arbitrary integers. H\ H The orbifold possesses deformation parameters or moduli which are continuously variable quantities corresponding to radii and angles de"ning the underlying torus. These parameters can be absorbed into the de"nition of the basis vectors e .

R X(z)R XM (w) (z ) (z )2/Z . 109) 344 D. Bailin, A. Love / Physics Reports 315 (1999) 285}408 Thus, R ln(Z ) can be derived if we can calculate g(z,w;z ). z )\I,, wPz   wPz . z )\l,,   In terms of the holomorphic function de"ned in Eq. 111) where P(z,w) is a polynomial quadratic in z and w separately,  P(z,w)" a wGzH . 112) GH G H The coe$cients a are determined by requiring that there is no simple pole for zPw and that the GH numerator of the double pole is 1. This "xes all coe$cients a except for a , a and a , for which GH    there are only two equations.

Bailin, A. Love / Physics Reports 315 (1999) 285}408 term may be extracted from a non-renormalisable coupling of the form an n#3 point function of the type 331 L> for which we need 1< (z ,z )< (z ,z )< (z ,z )< (z z )2< (z ,z )2 . 3. Space group selection rules For a non-zero correlation function, the product of space group elements associated with the twisted sector states involved should contain the identity element of the space group [78,120]. In particular, consider a 3-point function with the three states associated with the space group elements ( ,l ),( ,l ) and ( ,l ) where , and are point group elements and    l "(I!

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