[Paper Review] Spectrum of Heterotic String on Orbifold

Kang-Sin Choi|arXiv (Cornell University)|May 23, 2004

Mathematics and Applications3 citations

TL;DR

This paper derives the spectrum of heterotic strings compactified on orbifolds by leveraging affine Lie algebra structures and twisted current algebras, establishing a systematic rule linking conformal weight, mass, and abelian charges—particularly for twisted sector states, enabling efficient classification of physical states in the compactified theory.

ABSTRACT

We obtain the spectrum of heterotic string compactified on orbifolds, focusing on its algebraic structure. Affine Lie algebra provides its current algebra and representations. The twisted version of algebra is used in the homomorphism from the orbifold action to the group action. The relation between the conformal weight and the mass gives a handy rule for obtaining especially twisted sector states and abelian charges.

Motivation & Objective

• To understand the algebraic structure underlying the spectrum of heterotic strings on orbifolds.
• To identify how twisted current algebras arise from the orbifold group action and govern the spectrum.
• To derive a systematic method for computing conformal weights and abelian charges of twisted sector states.
• To establish a direct correspondence between mass, conformal weight, and gauge quantum numbers in the compactified theory.

Proposed method

• Utilizing affine Lie algebra to describe the current algebra and representations in the heterotic string compactification.
• Applying the twisted version of the affine algebra to model the action of the orbifold group on the internal degrees of freedom.
• Constructing a homomorphism from the orbifold group to the gauge group action via twisted current algebra representations.
• Deriving a rule that relates the conformal weight of a state to its mass and abelian charge, especially in twisted sectors.
• Using the algebraic structure to classify physical states, particularly those in the twisted sectors of the orbifold compactification.

Experimental results

Research questions

• RQ1 How does the affine Lie algebra structure govern the current algebra and representations in heterotic string compactification on orbifolds?
• RQ2 What is the role of the twisted current algebra in encoding the orbifold group action on the internal symmetry?
• RQ3 How can conformal weight and mass be systematically related to determine physical states in the twisted sectors?
• RQ4 What is the algebraic rule that connects conformal weight, mass, and abelian charges in the spectrum?
• RQ5 How does the homomorphism from the orbifold group to the gauge group action manifest in the spectrum?

Key findings

• The spectrum of the heterotic string on orbifolds is algebraically structured through affine Lie algebra representations.
• Twisted current algebras emerge naturally as a consequence of the orbifold group action on the internal degrees of freedom.
• A direct rule is established linking conformal weight, mass, and abelian charges, particularly for twisted sector states.
• The method enables efficient identification and classification of physical states in the twisted sectors.
• The homomorphism from the orbifold group to the gauge group action is realized through the representation theory of the twisted affine algebra.