Matching three-point functions of BMN operators at weak and strong coupling

Abstract

The agreement between string theory and field theory is demonstrated in the leading order by providing the first calculation of the correlator of three two-impurity BMN states with all non-zero momenta. The calculation is performed in two completely independent ways: in field theory by using the large-N perturbative expansion, up to the terms subleading in finite-size, and in string theory by using the Dobashi-Yoneya 3-string vertex in the leading order of the Penrose expansion. The two results come out to be completely identical.

HHL correlators, orbit averaging and form factors

“…The motivation for this paper, however, goes beyond just the strong coupling limit and involves the search for a framework which would naturally allow for treatment at any coupling. The most general framework for OPE coefficients would most probably be (light cone) string field theory (SFT) [35,56,57,58] (and numerous papers in the pp-wave era, in particular [59,60,61,62,63]) as generically the sizes of the three strings would be different. However it has been suggested [64,65] that a simpler framework might be the formfactor formalism, where the emission of the third string would be described in terms of a vertex operator insertion on the worldsheet.…”

On three-point functions in the AdS4/CFT3 correspondence

“…For ABJM theory three-point functions of chiral primaries are in general not protected so even considering just such operators would provide valuable new information. Some progress on the inclusion of loop corrections in the case of N = 4 SYM was recently achieved in [14,31,32,33,34].…”

On membrane interactions and a three-dimensional analog of Riemann surfaces

“…Such a potential solves the Laplace equation and satisfies all the boundary conditions. 12 The existence of this solution implies that if J i = (1, 1, 1, . .…”

“…A method to compare the cubic vertices in string theory to the corresponding conformal three-point functions in the CFT was discussed in [7], following a spacetime interpretation first proposed in [8]. Studies using other approaches can be found in [9][10][11][12][13][14]. Similar aspects have been extensively studied beyond the pp-wave approximation taking advantage of the integrability appearing in the analysis of the system.…”

“…The BPS (anti-)instantons are the configurations [17,18] which saturate the bound (2.10) and therefore satisfy the equations 12) with X m = 0 and Ψ = 0. In this paper, we refer to solutions of (2.12) in which one chooses the upper or lower signs as instantons or anti-instantons, respectively.…”