The Virasoro-Shapiro amplitude in AdS$_5\times$S$^5$ and level splitting of 10d conformal symmetry
| Autor: | Aprile, F., Drummond, J. M., Paul, H., Santagata, M. |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | JHEP 11 (2021) 109 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP11(2021)109 |
| Popis: | The genus zero contribution to the four-point correlator $\langle {\cal O}_{p_1}{\cal O}_{p_2}{\cal O}_{p_3}{\cal O}_{p_4}\rangle$ of half-BPS single-particle operators ${\cal O}_p$ in $\mathcal{N}=4$ super Yang-Mills at strong coupling computes the Virasoro-Shapiro amplitude of closed superstrings on $AdS_5\times S^5$. Combining Mellin space techniques, the large $p$ limit, and data about the spectrum of two-particle operators at tree level in supergravity, we design a bootstrap algorithm which heavily constrains its $\alpha'$ expansion. We use crossing symmetry, polynomiality in the Mellin variables and the large $p$ limit to stratify the Virasoro-Shapiro amplitude away from the ten-dimensional flat space limit. Then we analyse the spectrum of exchanged two-particle operators at fixed order in the $\alpha'$ expansion. We impose that the ten-dimensional spin of the spectrum visible at that order is bounded above in the same way as in the flat space amplitude. This constraint determines the Virasoro-Shapiro amplitude in $AdS_5\times S^5$ up to a small number of ambiguities at each order and we compute it explicitly for $(\alpha')^{5,6,7,8,9}$. As the order of $\alpha'$ grows, the ten dimensional spin grows, and the set of visible two-particle operators opens up. Operators illuminated for the first time receive a string correction to their anomalous dimensions. This correction is uniquely determined and lifts the residual degeneracy of tree level supergravity due to ten-dimensional conformal symmetry. We encode the lifting of the residual degeneracy in a characteristic polynomial. This object carries information about all orders in $\alpha'$.It is analytic in the quantum numbers, symmetric under an $AdS_5 \leftrightarrow S^5$ exchange, and it enjoys intriguing properties, which we explain and detail in various cases. Comment: 46 pages plus Appendices A and B; v2: 48 pages plus Appendices A and B, typos fixed, match with JHEP version; v3: added funding acknowledgement |
| Databáze: | arXiv |
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