Abstract
We disentangle the contribution of scalars to the OPE series of null hexagonal Wilson loops/MHV gluon scattering amplitudes in multicolour N=4 SYM. In specific, we develop a systematic computation of the SU(4) matrix part of the Wilson loop by means of Young tableaux (with several examples). Then, we use a peculiar factorisation property (when a group of rapidities becomes large) to deduce an explicit polar form. Furthermore, we emphasise the advantages of expanding the logarithm of the Wilson loop in terms of ‘connected functions’ as we apply this procedure to find an explicit strong coupling expansion (definitively proving that the leading order can prevail on the classical AdS5 string contribution).
Highlights
Introduction and summaryIn the last years there has been much interest in SU(Nc) N = 4 Super Yang-Mills (SYM) theory, especially in the so-called planar limit Nc → ∞, gY M → 0, and fixed ’t Hooft coupling λ ≡ NcgY2 M = 16π2g2 . (1.1)It cannot be clearer that we are interested in gauge theories for phenomenological reasons, there are at least two other valid motivations
The OPE series terms cannot be directly derived from the gauge or string theory, yet the integrability of the flux-tube dynamics spanned by the the Gubser, Klebanov and Polyakov (GKP) string [23] has given many ideas on their properties
The strong coupling behaviour of the quantum GKP dynamics shows at least two different regimes depending on the value of the rapidities
Summary
In usual theories like [56] the connected functions enjoy an exponential fall-off, whilst asymptotically free theories are endowed with a softer power-like decay at infinity: this makes the discussion more delicate because of the need of cut-offs in the next-to-leading orders (and the peculiar appearance of terms ∼ ln λ, cf infra formulæ (4.34-4.36)). The coordinates of the fields are the conformal ratios fixing the polygon. 4The latter assume a slightly more general form than that in [56]
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