Andrés Moreno, "A parabolic flow for the large volume heterotic G2 system"

vendredi 24 avr. 2026, 11:15 → 12:30 Europe/Paris

The solution of the Killing spinor equations (KSE) in the underlying manifold M are an important assumption in string theory, Depending on the manifold dimension, these equations are related with the existence of a geometric structure with a particular torsion. In dimension seven, these equations are related to the existence of a G2-structure φ ∈ Ω^3(M ), admitting a unique linear connection ∇ with totally skew-symmetric torsion Hφ, such that: ∇φ = 0 and dHφ = 0. The first equation is equivalent to d ∗ φ = θ ∧ ∗φ where θ is called the Lee form and ∗ φ is the Hodge dual 4-form of φ. In particular,
when θ = dϕ is non-zero, φ solves the KSE with exact Lee form.

In this talk, we introduce a geometric flow of G2-structures, which preserve the conformally coclosed condition and whose critical points are solutions of the KSE with exact Lee form, in particular, when M is compact, those critical points are torsion-free G2-structures. For this flow, we prove short-time existence and uniqueness of solutions, as well as Shi-type estimates for the flow, it leads to a general result on the convergence of nonsingular solutions.. Moreover, we consider a particular case of G2-structures with SU(3)-symmetry and for this Ansatz, the dimensional reduction for the flow equation becomes a coupled type IIA and type IIB flow for the SU(3)-structure. This is a joint work (arxiv: 2512.14317) with M. Garcia Fernandez (ICMAT), A. Payne (NC State) and J. Streets (UCI).