A Metric for Heterotic Moduli

Abstract

Heterotic vacua of string theory are realised, at large radius, by a compact threefold with vanishing first Chern class together with a choice of stable holomorphic vector bundle. These form a wide class of potentially realistic four-dimensional vacua of string theory. Despite all their phenomenological promise, there is little understanding of the metric on the moduli space of these. What is sought is the analogue of special geometry for these vacua. The metric on the moduli space is important in phenomenology as it normalises D-terms and Yukawa couplings. It is also of interest in mathematics, since it generalises the metric, first found by Kobayashi, on the space of gauge field connections, to a more general context. Here we construct this metric, correct to first order in alpha', in two ways: first by postulating a metric that is invariant under background gauge transformations of the gauge field, and also by dimensionally reducing heterotic supergravity. These methods agree and the resulting metric is Kahler, as is required by supersymmetry. Checking that the metric is in fact Kahler is quite intricate and uses the anomaly cancellation equation for the H-field, in an essential way. The Kahler potential nevertheless takes a remarkably simple form: it is Kahler potential for special geometry with the Kahler form replaced by the alpha'-corrected hermitian form.

57 pages; v2 blackboard bold font error fixed; v3 minor improvements, typos fixed, references added; v4 version for publication in CMP

References in corpus (4)

• Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua
• Stability Walls in Heterotic Theories
• The Revival of (0,2) Linear Sigma Models
• Recent Developments in (0,2) Mirror Symmetry

Cited by in corpus (21)

• Finite deformations from a heterotic superpotential: holomorphic Chern--Simons and an $L_{\infty }$ algebra
• The infinitesimal moduli space of heterotic $G_2$ systems
• The Universal Geometry of Heterotic Vacua
• On de Sitter Spacetime and String Theory
• Heterotic backgrounds via generalised geometry: moment maps and moduli
• Holomorphic string algebroids
• Nongeometric heterotic strings and dual F-theory with enhanced gauge groups
• Gauge theory for string algebroids
• On the Effective Field Theory of Heterotic Vacua
• Heterotic Quantum Cohomology
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• On ${\alpha }^{\prime }$-effects from $D$-branes in $4d\mathcal{N}=1$
• Superpotential of Three Dimensional $\mathcal{N}=1$ Heterotic Supergravity
• Matter Field Kahler Metric in Heterotic String Theory from Localisation
• Generalized Vanishing Theorems for Yukawa Couplings in Heterotic Compactifications
• Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces
• Eigenvalues and eigenforms on Calabi-Yau threefolds
• Small gauge transformations and universal geometry in heterotic theories
• Special Lagrangian cycles and Calabi-Yau transitions
• Chern-Simons Invariants and Heterotic Superpotentials
• Balanced and Aeppli Parameters for the Heterotic Moduli