Conjectures for large N superconformal chiral primary four point functions

Abstract

An expression for the four point function for 1 2 -BPS operators belonging to the [0, p, 0] SU4) representation in N = 4 superconformal theories at strong coupling in the large N limit is suggested for any p. It is expressed in terms of the four point integrals defined by integration over AdS 5 and agrees with, and was motivated by, results for p = 2, 3, 4 obtained via the AdS/CFT correspondence. Using crossing symmetry and unitarity, the detailed form is dictated by the requirement that at large N the contribution of long multiplets with twist less than 2p, which do not have anomalous dimensions, should cancel corresponding free field contributions.

Towards 4-point correlation functions of any 1 2 $$ \frac{1}{2} $$ -BPS operators from supergravity

“…Recently the authors of [4] conjectured an interesting formula for the Mellin representation of the four-point correlation function of arbitrary weight 1 2 -BPS operators in the supergravity limit. In addition to the expected OPE behavior in this limit and to the agreement with an earlier proposal [5] on the structure of the four-point correlation functions of equal weight Leaving technical complications out of the discussion, to derive the corresponding correlation function and in this way to prove the conjecture by [4], one has to use the quartic effective action for Kaluza-Klein modes of type IIB supergravity compactified on the fivesphere S 5 [6]. We recall that Here A exchange comprises the sum of all exchange graphs which are generated by cubic Lagrangian vertices involving two scalars s I and any other supergravity field which is…”

Loop corrections for Kaluza-Klein AdS amplitudes

“…This suggests that the sum may simplify if one pulls out factors made from the operator ∆ (8) . Indeed we find this is the case.…”

“…( 5.27) We remark that the double discontinuity of the correlator O 2 O 2 O 2 O 2 computed in [17] can similarly be simplified by using the same singlet channel ∆ (8) operator. For the other correlator, O 2 O 3 O 2 O 3 , the double discontinuity is given by…”

Analytic bootstrap at large spin

“…Applications have been found in diverse field theories ranging from supersymmetric conformal field theories [13][14][15][16][17] to the 3d-Ising model at criticality [18][19][20][21]. The lessons learnt using these methods transcend any underlying Lagrangian formulation and are hoped to be very general.…”