Derived deformation theory of heterotic G2 systems near the standard embedding
Abstract
We study heterotic G2 structures near a torsion-free standard embedding, to first order in α' and to all orders in formal deformations. The tangent connection is the Hull connection determined by the metric and flux. We construct a locally invertible family of differential operators relating the supersymmetry and instanton BPS equations to the Euler-Lagrange equations of the heterotic superpotential. Using this comparison and the physical gauge symmetries, we construct a homological vector field locally formally conjugate to the Hamiltonian vector field of the superpotential. On a closed manifold in the fixed gerbe sector, the torsion equation implies vanishing of the leading flux. We prove ellipticity of the linearized deformation complex with mixed differential-order weights and construct a finite-dimensional cyclic L∞ model with a formal effective potential.
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BibTeX
@misc{brongers2026derived,
title = {{Derived deformation theory of heterotic $G_2$ systems near the standard embedding}},
author = {Bram Brongers},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.35071},
eprint = {2609.35071},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35071},
}
RIS
TY - UNPB
TI - Derived deformation theory of heterotic G_2 systems near the standard embedding
AU - Bram Brongers
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2609.35071
UR - https://arxiv.org/abs/2609.35071
AB - We study heterotic G_2 structures near a torsion-free standard embedding, to first order in α' and to all orders in formal deformations. The tangent connection is the Hull connection determined by the metric and flux. We construct a locally invertible family of differential operators relating the supersymmetry and instanton BPS equations to the Euler-Lagrange equations of the heterotic superpotential. Using this comparison and the physical gauge symmetries, we construct a homological vector field locally formally conjugate to the Hamiltonian vector field of the superpotential. On a closed manifold in the fixed gerbe sector, the torsion equation implies vanishing of the leading flux. We prove ellipticity of the linearized deformation complex with mixed differential-order weights and construct a finite-dimensional cyclic L_∞ model with a formal effective potential.
ER -