The Veneziano amplitude in AdS$_5 \times$S$^3$ from an 8-dimensional effective action
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arXiv
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| Natura: | Preprint |
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2023
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| author | Glew, R. Santagata, M. |
| author_facet | Glew, R. Santagata, M. |
| contents | We study four-point functions of arbitrary half-BPS operators in a 4-dimensional $\mathcal{N}=2$ SCFT with flavour group $SO(8)$ at genus-zero and strong 't Hooft coupling, corresponding - via AdS/CFT - to the ($α'$ expansion of the) Veneziano amplitude on an AdS$_5 \times$S$^3$ background. We adapt a procedure first proposed by Abl, Heslop and Lipstein in the context of AdS$_5 \times$S$^5$, and postulate the existence of an effective action in terms of an $8$-dimensional scalar field valued in the adjoint of the flavour group. The various Kaluza-Klein correlators can then be computed by uplifting the standard AdS/CFT prescription to the full product geometry with AdS bulk-to-boundary propagators and Witten diagrams replaced by suitable AdS$_5 \times$S$^3$ versions. After elucidating the main features of the procedure, valid at all orders in $α'$, we show explicit results up to order $α'^{5}$. The results provide further evidence of a novel relation between AdS$\times$S and flat amplitudes - which made its first appearance in $\mathcal{N}=4$ SYM - that is perhaps the most natural extension of the well known flat-space limit proposed by Penedones to cases where AdS and S have the same radius. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01013 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Veneziano amplitude in AdS$_5 \times$S$^3$ from an 8-dimensional effective action Glew, R. Santagata, M. High Energy Physics - Theory We study four-point functions of arbitrary half-BPS operators in a 4-dimensional $\mathcal{N}=2$ SCFT with flavour group $SO(8)$ at genus-zero and strong 't Hooft coupling, corresponding - via AdS/CFT - to the ($α'$ expansion of the) Veneziano amplitude on an AdS$_5 \times$S$^3$ background. We adapt a procedure first proposed by Abl, Heslop and Lipstein in the context of AdS$_5 \times$S$^5$, and postulate the existence of an effective action in terms of an $8$-dimensional scalar field valued in the adjoint of the flavour group. The various Kaluza-Klein correlators can then be computed by uplifting the standard AdS/CFT prescription to the full product geometry with AdS bulk-to-boundary propagators and Witten diagrams replaced by suitable AdS$_5 \times$S$^3$ versions. After elucidating the main features of the procedure, valid at all orders in $α'$, we show explicit results up to order $α'^{5}$. The results provide further evidence of a novel relation between AdS$\times$S and flat amplitudes - which made its first appearance in $\mathcal{N}=4$ SYM - that is perhaps the most natural extension of the well known flat-space limit proposed by Penedones to cases where AdS and S have the same radius. |
| title | The Veneziano amplitude in AdS$_5 \times$S$^3$ from an 8-dimensional effective action |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2305.01013 |