Secret Symmetries of AdS/CFT

Abstract

We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.

Factorization and subtraction

“…Clearly, at higher orders this relatively straightforward procedure becomes much more intricate, due to the presence of a large number of overlapping singular regions. Furthermore, this sketchy formal treatment neglects the technical difficulties associated with the need to construct precise and efficient phase space mappings relating the radiative and the Born configurations: our viewpoint on these issues is discussed in [18]. In what follows, we focus on the general structure of the counterterm functions K m .…”

“…Clearly, what we have given here is just a set of definitions and prescriptions: they have the advantage of being valid to all perturbative orders and being universal across multi-particle massless scattering amplitudes; on the other hand, to build an actual subtraction algorithm, one still needs to work through the details of phase-space parametrisations, momentum mappings, and, of course, the necessary integrations of counterterms over the unresolved phase spaces. Our approach to these essential practical problems has been outlined in [18].…”

“…After pioneering results on jet production in electron-positron annihilation [15,16], several approaches have been developed to tackle the problem for hadron scattering; some have already been successfully deployed to selected processes at NNLO, while some are in different stages of development: several talks at this conference have discussed recent developments of the various proposed methods and their applications [17,18,19,20,21,22,23,24]. To give an extremely concise summary of the state of the art, we note that the first fully hadronic process to be studied at NNLO at the level of fully differential distributions was the production of top-antitop pairs [25,26], a seminal result achieved using a predominantly numerical subtraction scheme; processes with one final-state jet, or with electroweak final states, have subsequently been tamed using phase-space slicing methods such as N-Jettiness subtraction [27,28,29], or q T subtraction [30,31,32]; very recently, the first complete results for dijet production (in the planar limit) have been presented [33], using Antenna subtraction.…”