Deep inelastic scattering in conformal QCD

By L. Cornalba, M. Costa, J. Penedones. 2009

135 citations recorded by the source corpus.

We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study small-x deep inelastic scattering in $ \mathcal{N} = 4 $ SYM or in QCD assuming approximate conformal symmetry. After clarifying the nature of the Regge limit for a CFT correlator, we use its conformal partial wave expansion to obtain an impact parameter representation encoding the exchange of a spin j Reggeon for any value of the coupling constant. The CFT impact parameter space is the three-dimensional hyperbolic space H3, which is the impact parameter space for high energy scattering in the dual AdS space. We determine the small-x structure functions associated to the exchange of a Reggeon. We discuss unitarization from the point of view of scattering in AdS and comment on the validity of the eikonal approximation.We then focus on the weak coupling limit of the theory where the amplitude is dominated by the exchange of the BFKL pomeron. Conformal invariance fixes the form of the vector impact factor and its decomposition in transverse spin 0 and spin 2 components. Our formalism reproduces exactly the general results predict by the Regge theory, both for a scalar target and for γ* − γ* scattering. We compute current impact factors for the specific examples of $ \mathcal{N} = 4 $ SYM and QCD, obtaining very simple results. In the case of the R-current of $ \mathcal{N} = 4 $ SYM, we show that the transverse spin 2 component vanishes. We conjecture that the impact factors of all chiral primary operators of $ \mathcal{N} = 4 $ SYM only have components with 0 transverse spin.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fcb275f813325d84ec269bc8588928615d900377

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Citations in the corpus

4D scattering amplitudes and asymptotic symmetries from 2D CFT (2016, methodology): “Here the mechanics of this continuation, as well as our calculations in general, are greatly simplified by employing the elegant embedding formalism of [56–60].”
A natural language for AdS/CFT correlators (2011, background): “As explained in [54, 41], a spin-1 primary operator Aμ(x) is uplifted to a transverse spin-1 field AM(P ) on the light-cone of M, such that P AM(P ) = 0 , Aμ(x) = ∂P ∂xμ AM(P ) , (146)”
Light-ray operators in conformal field theory (2018, background): “One of the most important is the Regge limit of a time-ordered four-point function (figure 1) [1–6].”
Spinning conformal correlators (2011, background): “71) Hence we recover the counting already presented in [18].”
Towards Feynman rules for Mellin amplitudes in AdS/CFT (2011, unknown): “= 0 [30, 24].”
EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions (2016, methodology): “Recently, Penedones, Trevisani and Yamazaki [27] and Yamazaki [28] pointed out the relevance of the old mathematical work of Jantzen [29] to this problem.”
Spinning conformal blocks (2011, methodology): “This approach to CFT computations goes back to the work of Dirac [27], and has been used on and oﬀ since the 1970’s [1, 28, 29] (see also [30, 31] for recent work).”
Spinning AdS propagators (2014, methodology): “This fact has been explored in many places in the literature to simplify computations, including computations of correlation functions of higher spin fields [9, 10, 11], of conformal blocks for external operators with spin [12, 13], and of Witten diagrams to derive Feynman rules in Mellin space [14,”