A note on generalized twisted fields and autotopisms of translation planes

The first part of this paper is a discussion of autotopism groups of certain translation planes. The second part shows that there is a certain class of semifields of order q4 having nuclei of order q2 , and their translation planes are not desarguesian and not isomorphic to generalized twisted field planes.

TWISTED BOUNDARY CONDITIONS AND MATCHING TO THE EFFECTIVE FOUR-DIMENSIONAL THEORY

Nontrivial twisted boundary conditions associated with extra compact dimensions can produce an ambiguity in the value of the four-dimensional coupling constants of the renormalizable interactions of the twisted fields' zero-modes. Resolving this indeterminacy would require a knowledge of the exact form of the higher dimensional action including the coefficients of higher-dimensional operators. For the case of moderately sized extra dimensions, the uncertainty in the coupling constants can be of order one and may lead to modifications in the stability of the model.

EXPONENTIALLY SMALL COUPLINGS BETWEEN TWISTED FIELDS OF ORBIFOLD STRING THEORIES

We investigate the natural occurrence of exponentially small couplings in effective field theories deduced from higher-dimensional models. As a concrete example we calculate the coupling between twisted fields of the Z3 Abelian orbifold compactification of the heterotic string. These are described by an effective field theory coupling the ten-dimensional massless gauge bosons to the four-dimensional twisted fields. The propagation of massive winding modes between the fixed points of the orbifold induces exponentially small couplings between the massless twisted fields. The resulting small couplings have an exponential dependence on the mass of the intermediate states and the distance between the fixed points.

AN EXAMPLE OF HIGHER WEIGHT SUPERPOTENTIAL INTERACTION IN THE HETEROTIC STRING ON ORBIFOLDS

An explicit orbifold example of the nonzero correlation functions related to the additional contribution to the induced mass term for Higgs particles at low energies is given. We verify that they form finite-dimensional representations of the target space modular transformation SL 2(Z). This action of the modular group is shown to be consistent with its action on the fixed point set defining the twisted fields.