On categorification of Stokes coefficients in Chern-Simons theory
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916164185096192 |
|---|---|
| author | Gukov, Sergei Putrov, Pavel |
| author_facet | Gukov, Sergei Putrov, Pavel |
| contents | We consider a finite-dimensional oscillatory integral which provides a "finite-dimensional model" for analytically continued $SU(2)$ Chern-Simons theory on closed 3-manifolds that are described by plumbing trees. This model allows an efficient description of Stokes phenomenon for perturbative expansions in Chern-Simons theory around classical solutions - $SL(2,\mathbb{C})$ flat connections. Moreover, the Stokes coefficients can be categorified, i.e. promoted to graded vector spaces, in terms of this finite-dimensional model. At least naively, the categorification gives BPS spectrum of 5d maximally supersymmetric Yang-Mills theory on the 3-manifold times a line with appropriate boundary conditions. We also comment on necessity of taking into account "flat connections at infinity" to capture Stokes phenomenon for certain 3-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12128 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On categorification of Stokes coefficients in Chern-Simons theory Gukov, Sergei Putrov, Pavel High Energy Physics - Theory Mathematical Physics Geometric Topology Quantum Algebra Symplectic Geometry We consider a finite-dimensional oscillatory integral which provides a "finite-dimensional model" for analytically continued $SU(2)$ Chern-Simons theory on closed 3-manifolds that are described by plumbing trees. This model allows an efficient description of Stokes phenomenon for perturbative expansions in Chern-Simons theory around classical solutions - $SL(2,\mathbb{C})$ flat connections. Moreover, the Stokes coefficients can be categorified, i.e. promoted to graded vector spaces, in terms of this finite-dimensional model. At least naively, the categorification gives BPS spectrum of 5d maximally supersymmetric Yang-Mills theory on the 3-manifold times a line with appropriate boundary conditions. We also comment on necessity of taking into account "flat connections at infinity" to capture Stokes phenomenon for certain 3-manifolds. |
| title | On categorification of Stokes coefficients in Chern-Simons theory |
| topic | High Energy Physics - Theory Mathematical Physics Geometric Topology Quantum Algebra Symplectic Geometry |
| url | https://arxiv.org/abs/2403.12128 |