Finite deformations from a heterotic superpotential: holomorphic Chern--Simons and an $L_{\infty }$ algebra

Abstract

We consider finite deformations of the Hull--Strominger system. Starting from the heterotic superpotential, we identify complex coordinates on the off-shell parameter space. Expanding the superpotential around a supersymmetric vacuum leads to a third-order Maurer--Cartan equation that controls the moduli. The resulting complex effective action generalises that of both Kodaira--Spencer and holomorphic Chern--Simons theory. The supersymmetric locus of this action is described by an $L_3$ algebra.

65 pages, including 5 appendices

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Cited by in corpus (15)

• 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
• Heterotic Quantum Cohomology
• Unbroken $E_7\times E_7$ nongeometric heterotic strings, stable degenerations and enhanced gauge groups in F-theory duals
• Superpotential of Three Dimensional $\mathcal{N}=1$ Heterotic Supergravity
• Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces
• $\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $\sigma$-models
• Eigenvalues and eigenforms on Calabi-Yau threefolds
• Small gauge transformations and universal geometry in heterotic theories
• Topological G${}_2$ and Spin(7) strings at 1-loop from double complexes
• Chern-Simons Invariants and Heterotic Superpotentials
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• Balanced and Aeppli Parameters for the Heterotic Moduli