Modularity in $d > 2$ free conformal field theory
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917846796206080 |
|---|---|
| author | Lei, Yang van Leuven, Sam |
| author_facet | Lei, Yang van Leuven, Sam |
| contents | We derive new closed form expressions for the partition functions of free conformally-coupled scalars on $S^{2D-1}\times S^1$ which resum the exact high-temperature expansion. The derivation relies on an identification of the partition functions, analytically continued in chemical potentials and temperature, with multiple elliptic Gamma functions. These functions satisfy interesting modular properties, which we use to arrive at our expressions. We describe a geometric interpretation of the modular properties of multiple elliptic Gamma functions in the context of superconformal field theory. Based on this, we suggest a geometric interpretation of the modular property in the context of the free scalar CFT in even dimensions and comment on extensions to odd dimensions and free fermions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01567 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modularity in $d > 2$ free conformal field theory Lei, Yang van Leuven, Sam High Energy Physics - Theory Mathematical Physics We derive new closed form expressions for the partition functions of free conformally-coupled scalars on $S^{2D-1}\times S^1$ which resum the exact high-temperature expansion. The derivation relies on an identification of the partition functions, analytically continued in chemical potentials and temperature, with multiple elliptic Gamma functions. These functions satisfy interesting modular properties, which we use to arrive at our expressions. We describe a geometric interpretation of the modular properties of multiple elliptic Gamma functions in the context of superconformal field theory. Based on this, we suggest a geometric interpretation of the modular property in the context of the free scalar CFT in even dimensions and comment on extensions to odd dimensions and free fermions. |
| title | Modularity in $d > 2$ free conformal field theory |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2406.01567 |