Spectral Geometry of Heterotic Compactifications

TL;DR

This paper explores the geometric and algebraic structure of heterotic string compactifications using noncommutative geometry, revealing how gauge fields emerge from K-theory in the quantum geometry of these models.

Contribution

It introduces a spectral triple framework for heterotic compactifications, showing gauge fields originate from K-theory and low-energy sectors lack intrinsic gauge degrees of freedom.

Findings

Gauge fields vanish in low-energy sectors

Quantum geometry parallels superstring target spaces

Non-abelian gauge theories arise from K-theory

Abstract

The structure of heterotic string target space compactifications is studied using the formalism of the noncommutative geometry associated with lattice vertex operator algebras. The spectral triples of the noncommutative spacetimes are constructed and used to show that the intrinsic gauge field degrees of freedom disappear in the low-energy sectors of these spacetimes. The quantum geometry is thereby determined in much the same way as for ordinary superstring target spaces. In this setting, non-abelian gauge theories on the classical spacetimes arise from the K-theory of the effective target spaces.