2025/11/12 by Yalcinkaya, Eyup
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2511.09161
We explore the deformation theory of instantons on locally conformal (LC) Spin(7) manifolds. These structures, characterized by a non-parallel fundamental 4-form Φ satisfying dΦ= θ\wedge Φ, represent a significant, yet geometrically constrained, class of non-integrable G-structures. We analyze the infinitesimal deformation complex for Spin(7)-instantons in this setting. Our primary contribution is the reformulation of the linearized deformation equations -- comprising the linearized instanton condition and a gauge-fixing term -- using a t-parameter family of Dirac operators. We demonstrate that the t-dependent torsion terms arising from the Lee form θ cancel precisely. This unexpected simplification reveals that the deformation space H1 is governed entirely by the Levi-Civita geometry, effectively reducing the torsion-full problem to a more classical, torsion-free (Levi-Civita) setting. Using a Lichnerowicz-type rigidity theorem, we establish a general condition for an (LC) Spin(7)-instanton to be rigid (i.e., H1 = \0\). We apply this theory to the flat instanton (A=0) on known compact homogeneous (LC) Spin(7) manifolds and conclude that the flat instanton on these spaces is non-rigid, thus possessing a non-trivial moduli space.