Interactions of strings on a T-fold

TL;DR

This paper analyzes string interactions on T-folds using exact world-sheet methods, computing scattering amplitudes and revealing suppression and quantization effects related to T-duality twists.

Contribution

It provides the first explicit calculation of scattering amplitudes involving twisted and untwisted strings on T-folds, highlighting suppression and quantization phenomena.

Findings

Four-point amplitudes expressed with hypergeometric functions.

Three-point couplings suppressed by chiral momenta and quantized in 1/4 powers.

High-energy asymptotic behavior of amplitudes derived.

Abstract

We consider the interactions of strings on T-folds from the world-sheet point of view which are exact in $\alpha'$. As a concrete example, we take a model where the internal torus at the so(8) enhancement point is twisted by T-duality (T-folded), and compute the scattering amplitudes of a class of massless strings. The four-point amplitudes involving both twisted and untwisted strings are obtained in a closed form in terms of the hypergeometric function. By their factorization, the three-point coupling of the twisted and untwisted strings is found to be suppressed by the chiral momenta along the internal torus, and quantized in integer powers of 1/4. The asymptotic forms of the four-point amplitudes in high-energy limits are also obtained. Our results rely only on general properties of the asymmetric orbifold by the T-duality twist and of the Lie algebra lattice from the symmetry enhancement, and thus may be extended qualitatively to more general T-folds.