The Nahm transform of multi-fractional instantons
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916487001800704 |
|---|---|
| author | Anber, Mohamed M. Poppitz, Erich |
| author_facet | Anber, Mohamed M. Poppitz, Erich |
| contents | We embed the multi-fractional instantons of $SU(N)$ gauge theories on $\mathbb T^4$ with 't Hooft twisted boundary conditions into $U(N)$ bundles and use the Nahm transform to study the corresponding configurations on the dual $\widehat{\mathbb T}^4$. We first show that $SU(N)$ fractional instantons of topological charge $Q={r \over N}$, $r \in \{1, 2,...,N-1\}$, are mapped to fractional instantons of $SU(\widehat N)$ of charge $\widehat Q = {r \over \widehat N}$, where $\widehat N = N q_1 q_3 - r q_3 + q_1$ 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 $SU(\widehat N)$ configurations they map to. Both the $\mathbb T^4$ instantons and their $\widehat {\mathbb T}^4$ images are self-dual for appropriately tuned torus periods. The Nahm duality can be extended to tori with detuned periods, with detuning parameter $Δ$, mapping solutions with $Δ>0$ on $\mathbb T^4$ to ones with $\widehatΔ<0$ on $\widehat{\mathbb T}^4$. 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 $Δ\ne 0$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11962 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Nahm transform of multi-fractional instantons Anber, Mohamed M. Poppitz, Erich High Energy Physics - Theory High Energy Physics - Lattice Mathematical Physics We embed the multi-fractional instantons of $SU(N)$ gauge theories on $\mathbb T^4$ with 't Hooft twisted boundary conditions into $U(N)$ bundles and use the Nahm transform to study the corresponding configurations on the dual $\widehat{\mathbb T}^4$. We first show that $SU(N)$ fractional instantons of topological charge $Q={r \over N}$, $r \in \{1, 2,...,N-1\}$, are mapped to fractional instantons of $SU(\widehat N)$ of charge $\widehat Q = {r \over \widehat N}$, where $\widehat N = N q_1 q_3 - r q_3 + q_1$ 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 $SU(\widehat N)$ configurations they map to. Both the $\mathbb T^4$ instantons and their $\widehat {\mathbb T}^4$ images are self-dual for appropriately tuned torus periods. The Nahm duality can be extended to tori with detuned periods, with detuning parameter $Δ$, mapping solutions with $Δ>0$ on $\mathbb T^4$ to ones with $\widehatΔ<0$ on $\widehat{\mathbb T}^4$. 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 $Δ\ne 0$ 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. |
| title | The Nahm transform of multi-fractional instantons |
| topic | High Energy Physics - Theory High Energy Physics - Lattice Mathematical Physics |
| url | https://arxiv.org/abs/2411.11962 |