Towards the Virasoro-Shapiro amplitude in AdS5×S5

The genus zero contribution to the four-point correlator $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle $$ O p 1 O p 2 O p 3 O p 4 of half-BPS single-particle operators $$ {\mathcal{O}}_p $$ O p in $$ \mathcal{N} $$ N = 4 super Yang-Mills, at strong coupling, computes the Virasoro-Shapiro amplitude of closed superstrings in AdS5× S5. 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 α′ 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 α′ 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 AdS5× S5 up to a small number of ambiguities at each order. We compute it explicitly for (α′)5,6,7,8,9. As the order of α′ 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 which 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 α′. It is analytic in the quantum numbers, symmetric under an AdS5 ↔ S5 exchange, and it enjoys intriguing properties, which we explain and detail in various cases.

supporting

confidence: 53%

Section: Jhep11(2021)109mentioning

confidence: 63%

See 1 more Smart Citation

The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry

Aprile

Drummond

Paul

et al. 2021

“…This formula was proved in [14] by using the massless scattering smearing kernel (global AdS). We will actually follow the proof [14] in appendix C. It also passes verification to work for supersymmetric theories, see e.g., [27][28][29][30][31][32][33].…”

Section: • Masslessmentioning

confidence: 99%

Notes on flat-space limit of AdS/CFT

2021

Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin space, coordinate space, and partial-wave expansion. We explain the origin of momentum space as the smearing kernel in Poincare AdS, while the origin of latter three is the smearing kernel in global AdS. In Mellin space, we find a Mellin formula that unifies massless and massive flat-space limit, which can be transformed to coordinate space and partial-wave expansion. Furthermore, we also manage to transform momentum space to smearing kernel in global AdS, connecting all existed frameworks. Finally, we go beyond scalar and verify that $$ \left\langle VV\mathcal{O}\right\rangle $$ VV O maps to photon-photon-massive amplitudes.

“…This observation leads to a recursion relation that relates holographic correlators of operators with higher weights to the lowest-weight one, and the solution of the recursion relation yields precisely the formula originally given in [1]. This observation has been further explored for the holographic correlators in AdS 5 × S 5 beyond the tree-level approximation [12], and the fate of the hidden symmetry, when higher-derivative stringy effects are included, has been studied in [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Notes on gravity multiplet correlators in AdS3 × S3

Wen

Zhang

2021

We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in (2, 0) supergravity on AdS3× S3, with two operators in tensor multiplet and the other two in gravity multiplet. This is achieved by solving the recursion relation arising from a hidden six-dimensional conformal symmetry. We note the compact expression is obtained after carefully analysing the analytic structures of the correlators. Various limits of the correlators are studied, including the maximally R-symmetry violating limit and flat-space limit.