A worldsheet perspective on heterotic T-duality orbifolds

Asymmetric heterotic orbifolds are discussed from the worldsheet perspective. Starting from Buscher’s gauging of a theory of D compact bosons the duality covariant description of Tseytlin is obtained after a non-Lorentz invariant gauge fixing. A left-over of the gauge symmetry can be used to removed the doubled constant zero modes so that D physical target space coordinate remain. This can be thought of as the worldsheet realization of the strong constraint of double field theory. The extension of this description to the heterotic theory is straightforward as all results are written in terms of the invariant and the generalized metrics. An explicit method is outline how to obtain a generalized metric which is invariant under T-duality orbifold actions. It is explicitly shown how shift orbifolds lead to redefinitions of the Narain moduli. Finally, a number of higher dimensional T-folds are constructed including a novel asymmetric ℤ6 orbifold.

Heterotic orbifolds, reduced rank and SO(2n + 1) characters

The moduli space of the maximally supersymmetric heterotic string in [Formula: see text]-dimensional Minkowski space contains various components characterized by the rank of the gauge symmetries of the vacua they parametrize. We develop an approach for describing in a unified way continuous Wilson lines which parametrize a component of the moduli space, together with discrete deformations responsible for the switch from one component to the other. Applied to a component that contains vacua with [Formula: see text] gauge-symmetry factors, our approach yields a description of all backgrounds of the component in terms of free-orbifold models. The orbifold generators turn out to act symmetrically or asymmetrically on the internal space, with or without discrete torsion. Our derivations use extensively affine characters of [Formula: see text]. As a by-product, we find a peculiar orbifold description of the heterotic string in 10 dimensions, where all gauge degrees of freedom arise as twisted states, while the untwisted sector reduces to the gravitational degrees of freedom.

Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative scalar couplings of the form F(\Phi) (\nabla\Phi)^4F(Φ)(∇Φ)4 in a class of string vacua known as CHL \IZ_N heterotic orbifolds with NN prime, generalizing our previous work which dealt with the case of heterotic string on T^6T6. We derive the Ward identities that F(\Phi)F(Φ) must satisfy, and check that our formula obeys them. We analyze the weak coupling expansion of F(\Phi)F(Φ), and show that it reproduces the correct tree-level and one-loop contributions, plus an infinite series of non-perturbative contributions. Similarly, the large radius expansion reproduces the exact F^4F4 coupling in four dimensions, including both supersymmetric invariants, plus infinite series of instanton corrections from half-BPS dyons winding around the large circle, and from Taub-NUT instantons. The summation measure for dyonic instantons agrees with the helicity supertrace for half-BPS dyons in 4 dimensions in all charge sectors. In the process we clarify several subtleties about CHL models in D=4D=4 and D=3D=3, in particular we obtain the exact helicity supertraces for 1/2-BPS dyonic states in all duality orbits.