More dual string pairs from orbifolding

Abstract

We construct more dual pairs of type II-heterotic strings in four dimensions with N = 2, 1 spacetime supersymmetry. On the type II side the construction utilizes the various possible choices of K3 automorphisms with fixed points which transform the holomorphic two-form nontrivially, and rotation plus translation on T 2 . The CalabiYau orbifolds so obtained have non-zero Euler numbers, so quantum corrections exist on the type IIA strings. The heterotic string (asymmetric) orbifold duals are found which depend on going to the enhanced symmetry points. Some aspects of the construction are discussed including the role of the singularity and the possibility of going beyond the adiabatic argument. Many of these examples have also orientifold analogs.

Monstrous string-string duality

“…The heterotic soliton construction of Harvey and Strominger, and of Sen, provides a map between target space duality symmetries of the IIA theory and corresponding transformations on the world-sheet fields of the heterotic compactification. Provided such a symmetry is freely acting, one expects the theories obtained by orbifolding to provide additional strong/weak dual pairs [7,15,16,17,18,19,[20][21]. Thus, from this duality alone one can derive a remarkable web of strong/weak dualities in dimensions six and below.…”

On orientifold constructions of type IIA dual pairs

“…For that let us consider a T -duality element embedded in SO(5, 5) of Ref. [3] in the metricL and spinor multiplet basis, V −1 16 Pμ. Let us denote its vector and spinor representations as Ω t ,R s t .…”

“…To conclude, we have verified that for construction of typeIIA dual pairs through orientifolding, an explicit U-duality relationship for fields in the vector as well as spinor representation can be constructed. Unlike the pairing of type IIA on K3,with heterotic string on T 4 , [16] this relationship has been proven through the construction of appropriate gamma matrices. We can now follow Ref.…”

Orientifolds and type II dual pairs

“…Starting from the above heterotic-type II dual pair, many other nontrivial examples of the dual pairs of the heterotic-type II string theory were constructed in [10,11,12,13,14]. Many of these constructions are based on an adiabatic argument which implies that the two theories which are "strong-weak" dual of one another remain so during the process of compactifications on circles of arbitrary radii.…”

“…Some of these results have been checked by a direct calculation of the string loop amplitudes for the heterotic string theory and comparing them with the exact results of the type IIA theory [8,9]. Starting from the above heterotic-type II dual pair, many other nontrivial examples of the dual pairs of the heterotic-type II string theory were constructed in [10,11,12,13,14]. Many of these constructions are based on an adiabatic argument which implies that the two theories which are "strong-weak" dual of one another remain so during the process of compactifications on circles of arbitrary radii.…”