Kahler Potentials For Orbifolds With Continuous Wilson Lines And The Symmetries Of The String Action.

TL;DR

This paper derives the tree-level Kähler potentials for untwisted moduli in heterotic string orbifold compactifications with continuous Wilson lines using conformal field theory symmetries, constraining the effective action.

Contribution

It introduces a method to determine the form of the low-energy effective action for untwisted moduli based on symmetries of the underlying conformal field theory.

Findings

Derived explicit form of Kähler potentials for untwisted moduli.

Identified symmetries acting linearly on string coordinates and moduli.

Constrained the effective action up to a multiplicative factor.

Abstract

By employing the symmetries of the underlying conformal field theory, the tree-level K\"ahler potentials for untwisted moduli of the heterotic string compactifications on orbifolds with continuous Wilson lines are derived. These symmetries act linearly on bosonic (toroidal and $E_8\times E_8$ gauge) string coordinates as well as on the untwisted (toroidal and continuous Wilson lines) moduli; they correspond to the scaling of toroidal moduli, the axionic shift of toroidal moduli and the shift of the continuous Wilson line moduli. In turn such symmetries provide sufficient constraints to determine the form of the low-energy effective action associated with the untwisted moduli up to a multiplicative factor.