Analytic Torsion from Chern-Simons theory via the $(2,0)$-theory on Dicyclic Orbifolds of $S^3$
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913998385971200 |
|---|---|
| author | Albrychiewicz, Emil Valiente, Andrés Franco Ganor, Ori |
| author_facet | Albrychiewicz, Emil Valiente, Andrés Franco Ganor, Ori |
| contents | The Witten index of the $(2,0)$-theory compactified on spaces of the form $S^3/Γ\times S^2$, with a freely acting group $Γ$, and with external string sources implemented via timelike surface operator insertions, is expressed in terms of Ray-Singer torsion of $S^3/Γ$ and characters of irreducible representations of $Γ$. We compute it explicitly for the Dicyclic groups $Γ=\text{Dic}_k$. The torsion and characters are generally irrational numbers, but they nicely combine to an integer index. Alternatively, the Witten index can be computed from Chern-Simons theory on $S^2$, and Ray-Singer torsion on $S^3/\text{Dic}_k$ is thus computable from Chern-Simons theory. The matching of the Witten index calculated by these dual approaches reveals new details about the partition function of the $(2,0)$-theory with surface operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analytic Torsion from Chern-Simons theory via the $(2,0)$-theory on Dicyclic Orbifolds of $S^3$ Albrychiewicz, Emil Valiente, Andrés Franco Ganor, Ori High Energy Physics - Theory The Witten index of the $(2,0)$-theory compactified on spaces of the form $S^3/Γ\times S^2$, with a freely acting group $Γ$, and with external string sources implemented via timelike surface operator insertions, is expressed in terms of Ray-Singer torsion of $S^3/Γ$ and characters of irreducible representations of $Γ$. We compute it explicitly for the Dicyclic groups $Γ=\text{Dic}_k$. The torsion and characters are generally irrational numbers, but they nicely combine to an integer index. Alternatively, the Witten index can be computed from Chern-Simons theory on $S^2$, and Ray-Singer torsion on $S^3/\text{Dic}_k$ is thus computable from Chern-Simons theory. The matching of the Witten index calculated by these dual approaches reveals new details about the partition function of the $(2,0)$-theory with surface operators. |
| title | Analytic Torsion from Chern-Simons theory via the $(2,0)$-theory on Dicyclic Orbifolds of $S^3$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2502.18638 |