Supersymmetric localization and non-conformal $\mathcal{N}=2$ SYM theories in the perturbative regime
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arXiv
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| Format: | Preprint |
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2024
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| author | Billo', Marco Griguolo, Luca Testa, Alessandro |
| author_facet | Billo', Marco Griguolo, Luca Testa, Alessandro |
| contents | We examine the relation between supersymmetric localization on $\mathbb{S}^4$ and standard QFT results for non-conformal theories in flat space. Specifically, we consider 1/2 BPS circular Wilson loops in four-dimensional SU($N$) $\mathcal{N}$= 2 SYM theories with massless hypermultiplets in an arbitrary representation $\mathcal{R}$ such that the $β$-function is non-vanishing. On $\mathbb{S}^4$, localization maps this observable into an interacting matrix model. Although conformal symmetry is broken at the quantum level, we show that within a specific regime of validity the matrix model predictions are consistent with perturbation theory in flat space up to order $g^6$. In particular, at this order, localization predicts two classes of corrections proportional to $ζ(3)$ whose diagrammatic origins in field theory are remarkably different. One class of $ζ(3)$-like corrections emerges via interference effects between evanescent terms and the ultraviolet (UV) poles associated with the bare coupling constant, while the second one stems from a Feynman integral which retains the same form in flat space and on the sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supersymmetric localization and non-conformal $\mathcal{N}=2$ SYM theories in the perturbative regime Billo', Marco Griguolo, Luca Testa, Alessandro High Energy Physics - Theory We examine the relation between supersymmetric localization on $\mathbb{S}^4$ and standard QFT results for non-conformal theories in flat space. Specifically, we consider 1/2 BPS circular Wilson loops in four-dimensional SU($N$) $\mathcal{N}$= 2 SYM theories with massless hypermultiplets in an arbitrary representation $\mathcal{R}$ such that the $β$-function is non-vanishing. On $\mathbb{S}^4$, localization maps this observable into an interacting matrix model. Although conformal symmetry is broken at the quantum level, we show that within a specific regime of validity the matrix model predictions are consistent with perturbation theory in flat space up to order $g^6$. In particular, at this order, localization predicts two classes of corrections proportional to $ζ(3)$ whose diagrammatic origins in field theory are remarkably different. One class of $ζ(3)$-like corrections emerges via interference effects between evanescent terms and the ultraviolet (UV) poles associated with the bare coupling constant, while the second one stems from a Feynman integral which retains the same form in flat space and on the sphere. |
| title | Supersymmetric localization and non-conformal $\mathcal{N}=2$ SYM theories in the perturbative regime |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.11222 |