Unitarity methods in AdS/CFT

Abstract

We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and show how the conformal partial wave decomposition of the amplitudes may be efficiently computed by gluing lower-loop amplitudes. A central role is played by the double discontinuity of the amplitude, which has a direct relation to these cuts. We then exhibit a precise, intuitive map between the diagrammatic approach in the bulk using cutting and gluing, and the algebraic, holographic unitarity method of [1] that constructs the non-planar correlator from planar CFT data. Our analysis focuses mostly on four-point, one-loop diagrams -we compute cuts of the scalar bubble, triangle and box, as well as some one-particle reducible diagrams -in addition to the five-point tree and four-point double-ladder. Analogies with S-matrix unitarity methods are drawn throughout.

AdS/CFT unitarity at higher loops: high-energy string scattering

“…Diagrammatically, we are gluing two tree-level diagrams in the bulk by leveraging crossing symmetry on the boundary, see figure 5. In the bulk, the action of dDisc t can be visualized as projecting onto internal, horizontal line cuts, or the [φψ] n,J double-trace operators [58].…”

Spinor-helicity formalism for massless fields in AdS4 III: contact four-point amplitudes

“…See, for example,[9] for a classical review on the flat space S-matrix and its analytic structure. Analytic structure of AdS Witten diagrams has been studied in various representations and in many cases it is well understood; see[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] for a far from complete list of references. These achievements were used, in particular, for bootstrapping holographic amplitudes in type-IIB supergravity[27] and for computing the associated loop corrections from the dispersion relations[28,29].…”

Boundary correlators in WZW model on AdS2

“…summing half of the two residues at t = t ± z ). 30 For ω > 0, it reads 12) and thus implies again (5.10).…”

“…19 We first integrate over x and then add and subtract the leading term of the y → ∞ expansion. 20 For some recent discussions of one-loop self-energy corrections in AdS see [28][29][30].…”

“…Here and in the following, integrals z are restricted to the AdS2 region, i.e. z ≥ 0 30. At this stage this is just a formal prescription.…”