Cyclic L3 Models and Holomorphic Reduction in Heterotic G2 Deformation Theory
Abstract
We construct a finite cyclic L3 presentation (that is, a cyclic L∞ algebra with brackets vanishing above arity three) of the variational deformation theory defined by the heterotic G2 superpotential near a torsion-free standard embedding, to first order in α'. Auxiliary fields for the inverse coframe, spinor derivative, flux and induced tangent connection give a shifted-cotangent Hamiltonian of degree at most four. Eliminating the auxiliary fields recovers the physical functional. On the flat seven-torus, this functional has a nonzero quintic Taylor coefficient in local physical spinor coordinates. For Y=S1× X, with X a Calabi--Yau threefold, we restrict to the product locus with horizontal gauge and gerbe data. The functional reduces to $ \frac L4\operatorname{Im}\int_X(H+i\,dω)\wedgeΩ, $ where L is the circle length and Ω=e−2ΦΨ is the weighted complex volume. The induced SU(3) structure selects a Hermitian tangent Courant subalgebroid. Transverse isotropic lifts in its complexification encode the holomorphic connection and string equations, together with the induced tangent connection, weighted canonical line and gerbe hierarchy. Their Taylor brackets form an L3 algebra whose string part agrees with the known holomorphic heterotic algebra. We then show that this holomorphic theory is obtained by characteristic Hamiltonian reduction of a finite contractible stabilization of the product variational theory, in every cochain degree. While the quotient captures the holomorphic equations, conformal balance, gauge primitivity and leading-flux admissibility are additional conditions on a real representative.
Related
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BibTeX
@misc{brongers2026cyclic,
title = {{Cyclic $L_3$ Models and Holomorphic Reduction in Heterotic $G_2$ Deformation Theory}},
author = {Bram Brongers},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03301},
eprint = {2610.03301},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03301},
}
RIS
TY - UNPB
TI - Cyclic L_3 Models and Holomorphic Reduction in Heterotic G_2 Deformation Theory
AU - Bram Brongers
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03301
UR - https://arxiv.org/abs/2610.03301
AB - We construct a finite cyclic L_3 presentation (that is, a cyclic L_∞ algebra with brackets vanishing above arity three) of the variational deformation theory defined by the heterotic G_2 superpotential near a torsion-free standard embedding, to first order in α'. Auxiliary fields for the inverse coframe, spinor derivative, flux and induced tangent connection give a shifted-cotangent Hamiltonian of degree at most four. Eliminating the auxiliary fields recovers the physical functional. On the flat seven-torus, this functional has a nonzero quintic Taylor coefficient in local physical spinor coordinates. For Y=S^1× X, with X a Calabi--Yau threefold, we restrict to the product locus with horizontal gauge and gerbe data. The functional reduces to $ \frac L4\operatorname{Im}\int_X(H+i\,dω)\wedgeΩ, $ where L is the circle length and Ω=e^−2ΦΨ is the weighted complex volume. The induced SU(3) structure selects a Hermitian tangent Courant subalgebroid. Transverse isotropic lifts in its complexification encode the holomorphic connection and string equations, together with the induced tangent connection, weighted canonical line and gerbe hierarchy. Their Taylor brackets form an L_3 algebra whose string part agrees with the known holomorphic heterotic algebra. We then show that this holomorphic theory is obtained by characteristic Hamiltonian reduction of a finite contractible stabilization of the product variational theory, in every cochain degree. While the quotient captures the holomorphic equations, conformal balance, gauge primitivity and leading-flux admissibility are additional conditions on a real representative.
ER -