Abstract
We study instanton corrections to four-point correlation correlation function of half-BPS operators in mathcal{N} = 4 SYM in the light-cone limit when operators become null separated in a sequential manner. We exploit the relation between the correlation function in this limit and light-like rectangular Wilson loop to determine the leading instanton contribution to the former from the semiclassical result for the latter. We verify that the light-like rectangular Wilson loop satisfies anomalous conformal Ward identities nonperturbatively, in the presence of instantons. We then use these identities to compute the leading instanton contribution to the light-like cusp anomalous dimension and to anomalous dimension of twist-two operators with large spin.
Highlights
Perturbative contribution to Gn for finite N and supplement it with instanton corrections
We study instanton corrections to four-point correlation correlation function of half-BPS operators in N = 4 SYM in the light-cone limit when operators become null separated in a sequential manner
We demonstrated in the previous section that the leading light-cone asymptotics of the correlation function G4 is described by light-like rectangular Wilson loop W4
Summary
Where each fluctuation brings in the factor of g2 Comparing this relation with (1.1) we find that the first three terms in the expansion of the instanton induced function Φn(u, v; g2) in powers of g2 should vanish in the light-cone limit u, v → 0, in the one-instanton sector at least. To the leading order in g2, the dominant contribution to (2.11) comes from Feynman diagrams shown in figure 1 (b) They contain four scalar propagators connecting the points xi and xi+1. Denoting the scalar propagator in the instanton background as D(xi, xi+1), we obtain the following result for the correlation function in the light-like limit. Inst denotes integration over the collective coordinates of instantons with the measure (2.7) This result is rather general and it holds for multi-instanton contribution to G4 in N = 4 SYM with an arbitrary gauge group. The contribution from this region, denoted by J in (1.3), can be determined from the crossing symmetry of G4 in the same way as it was done in perturbation theory [20]
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