The Nahm transform of multi-fractional instantons

A bstract We embed the multi-fractional instantons of SU( N ) gauge theories on $$ {\mathbbm{T}}^4 $$ T 4 with ’t Hooft twisted boundary conditions into U( N ) bundles and use the Nahm transform to study the corresponding configurations on the dual $$ {\hat{\mathbbm{T}}}^4 $$ T ̂ 4 . We first show that SU( N ) fractional instantons of topological charge $$ Q=\frac{r}{N},r\in \left\{1,2,\dots, N-1\right\} $$ Q = r N , r ∈ 1 2 … N − 1 , are mapped to fractional instantons of SU( $$ \hat{N} $$ N ̂ ) of charge $$ \hat{Q}=\frac{r}{\hat{N}} $$ Q ̂ = r N ̂ , where $$ \hat{N} $$ N ̂ = Nq 1 q 3 − rq 3 + q 1 and q 1 , 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( $$ \hat{N} $$ N ̂ ) configurations they map to. Both the $$ {\mathbbm{T}}^4 $$ T 4 instantons and their $$ {\hat{\mathbbm{T}}}^4 $$ T ̂ 4 images are self-dual for appropriately tuned torus periods. The Nahm duality can be extended to tori with detuned periods, with detuning parameter ∆, mapping solutions with ∆ > 0 on $$ {\mathbbm{T}}^4 $$ T 4 to ones with $$ \hat{\Delta } $$ ∆ ̂ < 0 on $$ {\hat{\mathbbm{T}}}^4 $$ T ̂ 4 . We also recall that f

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.