2024/07/08 by Jesse Madnick, Madnick, Jesse, Emily Autumn Windes +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2407.06412
openalex publication_date 2024/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The real Fourier-Mukai (RFM) transform relates calibrated graphs to so-called "deformed instantons" on Hermitian line bundles. We show that under the RFM transform, complex Lagrangian graphs in R2n × T2n correspond to Sp(n)-instantons over R2n × (T2n)^*. In other words, the deformed Sp(n)-instanton equation coincides with the usual Sp(n)-instanton equation. Motivated by this observation, we study Sp(n)-instantons on hyperkahler manifolds X4n, with an emphasis on conical singularities. First, when X = C(M) is a hyperkahler cone, we relate Sp(n)-instantons on X to tri-contact instantons on the 3-Sasakian link M and consider various dimensional reductions. Second, when X is an asymptotically conical (AC) hyperkahler manifold of rate ν≤ -(2)/(3)(2n+1), we prove a Lewis-type theorem to the following effect: If the set of AC Sp(n)-instantons is non-empty, then every AC Hermitian Yang-Mills connection over X with sufficiently fast decay at infinity is an Sp(n)-instanton.