We calculate four classes of high energy massive string scattering amplitudes of fermionic string theory at arbitrary mass levels in the Regge regime (RR). We show that all four leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind.Based on the summation algorithm of a set of extended signed Stirling number identities, we show that all four ratios calculated previously by the method of decoupling of zero-norm states among scattering amplitudes in the Gross Regime (GR) can be extracted from this Kummer function in the RR. Finally, we conjecture and give evidences that the existence of these four GR ratios in the RR persists to subleading orders in the Regge expansion of all high energy fermionic string scattering amplitudes. * Electronic address: hesong@ihep.ac.cn † Electronic address:
We classify compactification lattices for supersymmetric Z 2 × Z 2 orbifolds. These lattices include factorisable as well as non-factorisable six-tori. Different models lead to different numbers of fixed points/tori. A lower bound on the number of fixed tori per twisted sector is given by four, whereas an upper bound consists of 16 fixed tori per twisted sector. Thus, these models have a variety of generation numbers. For example, in the standard embedding, the smallest number of net generations among these classes of models is equal to six, while the largest number is 48. Conditions for allowed Wilson lines and Yukawa couplings are derived.
We construct two more supersymmetric E6 grand unified models with three generations within the framework of Z12 asymmetric orbifold compactification of the heterotic string theory. Such an asymmetric orbifold is missing in the classification in the literature, which concludes that only one E6 model is possible. In both of the new models, an adjoint Higgs field is obtained in virtue of the diagonal embedding method. This method mods out the three E6 factors of an even selfdual momentum-lattice by a permutation symmetry. In order to realize the (E6) 3 even self-dual lattice, we utilize the lattice engineering technique. Among the eight possible orbifold actions in our setup, two lead to new E6 models. Though these models still share the unsatisfactory issues with the known one, our discovery raises hopes that excellent models that solve all the problems in the supersymmetric grand unified models will be found in this framework.
We provide a new class of Z N × Z M heterotic orbifolds on non-factorizable tori, whose boundary conditions are defined by Lie lattices. Generally, point groups of these orbifolds are generated by Weyl reflections and outer automorphisms of the lattices. We classify abelian orbifolds with and without discrete torsion. Then we find that some of these models have smaller Euler numbers than those of models on factorizable tori T 2 × T 2 × T 2 . There is a possibility that these orbifolds provide smaller generation numbers of N = 1 chiral matter fields than factorizable models. *
We investigate Type II orientifolds on non-factorizable torus with and
without its oribifolding. We explicitly calculate the Ramond-Ramond tadpole
from string one-loop amplitudes, and confirm that the consistent number of
orientifold planes is directly derived from the Lefschetz fixed point theorem.
We furthermore classify orientifolds on non-factorizable Z_N x Z_M orbifolds,
and construct new supersymmetric Type IIA orientifold models on them.Comment: 42 pages, 3 figures, v2: typos corrected, references added, version
to appear in Nucl. Phys.
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