Unmixing supergravity

Abstract

Abstract:We examine the double-trace spectrum of N = 4 super Yang-Mills theory in the supergravity limit. At large N double-trace operators exhibit degeneracy. By considering free-field and tree-level supergravity contributions to four-point functions of half-BPS operators we resolve the degeneracy for a large family of double-trace operators. The mixing problem reveals a surprisingly simple structure which allows us to obtain their three-point functions at leading order in the large N expansion as well as their leading anomalous dimensions.

Loop corrections for Kaluza-Klein AdS amplitudes

“…The relevant explicit formulas for the anomalous dimensions and three-point functions of doubletrace operators were obtained by considering multiple correlators which exhibit the same exchanged operators in their OPE decompositions [18]. Such data is available due to a remarkably compact formula [12] for all four-point tree-level scattering processes of graviton multiplets or their associated Kaluza-Klein modes which are present in the five-dimensional bulk due to the reduction from ten dimensions on S 5 .…”

“…Here we will summarise the results obtained in [17,18] which allowed for the bootstrapping of the one-loop four-graviton amplitude. Firstly we may consider the following set of double-trace operators K t,l,n,i , labelled by i which runs from 1 to (t − n − 1), t,l,n,i = − 2(t − n − 1)(t) 2 (t + n + 2)(t + l − n)(t + l + 1) 2 (t + l + n + 3) (l + 2i + n − 1) 6 , (…”

“…the case n = 0 above) were needed together with the results for the leading order threepoint functions O 2 O 2 K t,l,0,i , for which we also gave a closed form expression in [17,18], O 2 O 2 K t,l,0,i 2 = 8(t + l + 1)! 2 t!…”

“…However, this problem can be overcome and in fact it has been explicitly solved in [18] by considering the more general family of correlators…”

“…In fact, there is a conceptually simpler way to solve this equation. As outlined in [18] the entire superblock formalism can be bosonised. Since the Young tableau has height p we can use bosonised GL(p, p) blocks described in [18,24] for which 2…”