All tree-level correlators in AdS5×S5 supergravity: hidden ten-dimensional conformal symmetry

Abstract

We study correlators of four protected (half-BPS) operators in strongly coupled supersymmetric Yang-Mills theory. These are dual to tree-level supergravity amplitudes on AdS 5 ×S 5 for various spherical harmonics on the five-sphere. We use conformal field theory methods, in particular a recently obtained Lorentzian inversion formula, to analytically bootstrap these correlators. The extracted 1/N 2 double-trace anomalous dimensions confirm a simple pattern recently conjectured by Aprile, Drummond, Heslop and Paul. We explain this pattern by an unexpected ten-dimensional conformal symmetry which appears to be enjoyed by tree-level supergravity (or a suitable subsector of it). The symmetry combines all spherical harmonics into a single ten-dimensional object, and yields compact expressions for the leading logarithmic part of any half-BPS correlator at each loop order. arXiv:1809.09173v1 [hep-th] 24 Sep 2018A Basic inversion integrals 37 B Superconformal blocks, and weak coupling correlator to order 1/c 38 B.1 Weak coupling limit 39 C Ten-dimensional conformal blocks at the unitarity bound 40

One-loop amplitudes in AdS5×S5 supergravity from $$ \mathcal{N} $$ = 4 SYM at strong coupling

“…The eigenvectors however, are ambiguous if there are repeated eigenvalues, as turns out to be the case here [8]. This is the aforementioned degeneracy of anomalous dimensions, which is consequence of a surprising physical statement about tree-level physics: There is a hidden ten-dimensional conformal symmetry which prevents the spectrum from being fully unmixed at tree-level [9].…”

“…In fact a ten-dimensional conformal structure observed in [9] was found to give a direct formula for these leading logs. We checked in many cases that our results agree, and we postpone to Section 6 a more detailed description of this ten-dimensional structure.…”

“…1). 9 Compared to [8] we added a factor of 2 in the definition of δ For simplicity assume p 1 + p 2 ≥ p 3 + p 4 (the other case is similar), then (75) becomes…”

“…Recall that the SCPW coefficients L (1) appearing in (99) are determined by summing contributions of D (1) p , and connected free theory, as in (68). A general formula for connected free theory at order 1/N 2 can be obtained using results in [8], and was presented already in [9]. In our notation, it is recorded in Appendix B.1.…”

“…Finally, we understood how to deal with the SCPW coefficient of long operators at the unitarity bound in (111). We emphasize that even though the leading log discontinuity can be obtained more elegantly by using the hidden symmetry of [9], our approach here allows us to go beyond that, and compute M (2) and L (2) , which are very important pieces of our bootstrap program.…”