By Bailin, Love.
The compactification of the heterotic string concept on a six-dimensional orbifold is beautiful theoretically, because it allows the entire decision of the emergent 4-dimensional powerful supergravity thought, together with the gauge workforce and subject 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, masking 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 lots and combining; the calculation of the Kahler strength and its string loop threshold corrections; and the decision of the non-perturbative potent capability for the moduli bobbing up from hidden quarter gaugino condensation, and its reference to supersymmetry breaking. We finish with a short dialogue of the relevance of weakly coupled string conception within the gentle of modern advancements at the strongly coupled concept.
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Additional info for Orbifold compactifications of string theory
56) where, in each case, is an arbitrary lattice vector. Strictly, if the complex plane in question is, for example, the 1#i2 plane, then we need the component of (1! f # ), on the 1#i2 ? @ direction to give v for X> . 55) now determines the constant a as follows. For convenience, take z "0, z "1, z "z "R , using SL(2,C) symmetry. Then, using the integral ! z ) I>l , a" . 59) Consequently, after performing the dz, using Appendix A of , Z (with the index i sup pressed) is given by Eq.
Bailin, A. Love / Physics Reports 315 (1999) 285}408 require that RXG/Rz and RXG/Rz are functions of z and z alone, respectively, which must be chosen to respect the boundary conditions implicit in the operator product expansions (OPEs) with the twist "elds. These OPEs may be deduced from the mode expansions of the string degrees of freedom. If we write R i i L\I, z\ L\I, ! k/N) (n#k/N) 2 L L where and are oscillator modes, then for zP0, RX RX i " 0+! 50) dropping the annihilation operator term, and so RX RX i " 2" (0,0)"02&!
Also, from Eq. 56) Z & exp v"(I! f # ) . 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 .
Orbifold compactifications of string theory by Bailin, Love.