T Duality Between Perturbative Characters of $E_8\otimes E_8$ and SO(32) Heterotic Strings Compactified On A Circle

TL;DR

This paper explores T duality between $E_8\otimes E_8$ and SO(32) heterotic strings on a circle, highlighting the role of Wilson lines and an intermediate twisted compactification that maintains modular invariance.

Contribution

It introduces a new perspective on T duality involving Wilson lines and an intermediate theory with disentangled duality transformations, extending previous work on type II strings.

Findings

Wilson lines are crucial for T duality in heterotic strings.

An intermediate theory with twisted compactification exists, linking different lattice descriptions.

Modular invariance is preserved through an interplay of three modular group representations.

Abstract

Characters of $E_8\otimes E_8$ and SO(32) heterotic strings involving the full internal symmetry Cartan subalgebra generators are defined after circle compactification so that they are T dual. The novel point, as compared with an earlier study of the type II case (hep-th/9707107), is the appearence of Wilson lines. Using SO(17,1) transformations between the weight lattices reveals the existence of an intermediate theory where T duality transformations are disentangled from the internal symmetry. This intermediate theory corresponds to a sort of twisted compactification of a novel type. Its modular invariance follows from an interesting interplay between three representations of the modular group.