The scheme independent 3-sphere free energy is not a monotone F-function
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911698106974208 |
|---|---|
| author | Santoni, Giacomo Scardino, Francesco |
| author_facet | Santoni, Giacomo Scardino, Francesco |
| contents | We study the natural scheme-independent quantity obtained from the three-sphere partition function of a $(2+1)$-dimensional quantum field theory by removing all local counterterm ambiguities. At conformal fixed points this quantity equals the standard $F$-theorem invariant. Conformal perturbation theory shows that it locally decreases at $O(g^2)$ under any relevant scalar deformation of a three-dimensional CFT. However, an exact analysis of the free massive scalar on $S^3$ shows that this sphere-free-energy interpolant is not monotone along the full renormalization-group flow: it dips below its infrared value and then returns to it. Thus the natural counterterm-subtracted quantity built from sphere thermodynamics is not, by itself, a monotone $F$-function. We trace the obstruction to the second-order differential operator required to eliminate the local ambiguities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09799 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The scheme independent 3-sphere free energy is not a monotone F-function Santoni, Giacomo Scardino, Francesco High Energy Physics - Theory We study the natural scheme-independent quantity obtained from the three-sphere partition function of a $(2+1)$-dimensional quantum field theory by removing all local counterterm ambiguities. At conformal fixed points this quantity equals the standard $F$-theorem invariant. Conformal perturbation theory shows that it locally decreases at $O(g^2)$ under any relevant scalar deformation of a three-dimensional CFT. However, an exact analysis of the free massive scalar on $S^3$ shows that this sphere-free-energy interpolant is not monotone along the full renormalization-group flow: it dips below its infrared value and then returns to it. Thus the natural counterterm-subtracted quantity built from sphere thermodynamics is not, by itself, a monotone $F$-function. We trace the obstruction to the second-order differential operator required to eliminate the local ambiguities. |
| title | The scheme independent 3-sphere free energy is not a monotone F-function |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.09799 |