2024/11/18 by Mohamed M. Anber, Anber, Mohamed M., Erich Poppitz +1 · 1 citation
Engineering · Mathematics · #Advanced Control Systems Design #FOS: Physical sciences #Fractional Differential Equations Solutions #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2411.11962
openalex publication_date 2024/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We embed the multi-fractional instantons of SU(N) gauge theories on \mathbb T4 with 't Hooft twisted boundary conditions into U(N) bundles and use the Nahm transform to study the corresponding configurations on the dual \widehat\mathbb T4. We first show that SU(N) fractional instantons of topological charge Q=r \over N, r ∈ \1, 2,...,N-1\, are mapped to fractional instantons of SU(\widehat N) of charge \widehat Q = r \over \widehat N, where \widehat N = N q1 q3 - r q3 + q1 and q1,3 are integer-quantized U(1) fluxes. We then explicitly construct the Nahm transform of constant field strength fractional instantons of SU(N) and find the SU(\widehat N) configurations they map to. Both the \mathbb T4 instantons and their \widehat \mathbb T4 images are self-dual for appropriately tuned torus periods. The Nahm duality can be extended to tori with detuned periods, with detuning parameter Δ, mapping solutions with Δ>0 on \mathbb T4 to ones with \widehatΔ<0 on \widehat\mathbb T4. We also recall that fractional instantons appear in string theory precisely via the U(N) embedding, suggesting that studying the end point of tachyon condensation for Δ≠ 0 is needed -- and is perhaps feasible in a small-Δ expansion, as in field theory studies -- in order to understand the appearance and role of fractional instantons in D-brane constructions.