Abstract
We describe a new approach to computing the chiral part of correlation functions of stress-tensor supermultiplets in N=4 SYM that relies on symmetries, analytic properties and the structure of the OPE only. We demonstrate that the correlation functions are given by a linear combination of chiral N=4 superconformal invariants accompanied by coefficient functions depending on the space-time coordinates only. We present the explicit construction of these invariants and show that the six-point correlation function is fixed in the Born approximation up to four constant coefficients by its symmetries. In addition, the known asymptotic structure of the correlation function in the light-like limit fixes unambiguously these coefficients up to an overall normalization. We demonstrate that the same approach can be applied to obtain a representation for the six-point NMHV amplitude that is free from any auxiliary gauge fixing parameters, does not involve spurious poles and manifests half of the dual superconformal symmetry.
Highlights
We describe a new approach to computing the chiral part of correlation functions of stress-tensor supermultiplets in N = 4 SYM that relies on symmetries, analytic properties and the structure of the OPE only
As was explained in the previous subsection, the general expression for the correlation function Gn;p is given by a linear combination of chiral N = 4 superconformal invariants In;p accompanied by ρ-independent coefficient functions fn;p
We have studied the chiral sector of the correlation functions of stress-tensor supermultiplets in N = 4 SYM in the analytic superspace formulation [26,27,28]
Summary
Let us recall the properties of the stress-tensor supermultiplet. Its lowest component is the half-BPS scalar operator O20′(x, y) = tr ΦI ΦJ Y I Y J built from six real scalars ΦI (with I = 1, . . . , 6). The operator O20′(x, y) is annihilated by half of the Poincare supercharges, so that the stress-tensor multiplet satisfies a half-BPS shortening condition. The supercurrent T depends on half of the Grassmann variables, ραa = θαAu+Aa = θαa + θαa′ yaa′ , ραa′ = θαAu ̄A−a′ = θaα′ + yaa′ θaα ,. Where the harmonic variables u+Aa and uA−a′ (with the composite SU(4) index A = (a, a′)) parametrise the coset SU(4)/(SU(2) × SU(2) × U(1)) (or rather its complexification). In the chiral sector the supercurrent T = T (x, y, ρ) depends on the four Grassmann variables ραa (with α, a = 1, 2) as well as on the bosonic coordinates xαα and yaa′. The supercurrent T (x, y, ρ) transforms covariantly under the N = 4 superconformal algebra and has conformal weight.
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