Computing three-point functions for short operators

Abstract

Abstract:We compute the three-point structure constants for short primary operators of N = 4 super Yang-Mills theory to leading order in 1/ √ λ by mapping the problem to a flat-space string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We then compute the three-point functions for any combination of chiral and non-chiral primaries, with the non-chiral primaries all dual to string states at the first massive level. Along the way we find many cancellations that leave us with simple expressions, suggesting that integrability is playing an important role.

Analytic bounds and emergence of AdS2 physics from the conformal bootstrap

“…The only zero of ω ∆ ψ (∆) in this region occurs at some non-integer value ∆ 0 . We will see in section 6 that 17) which will be crucial to make contact with the flat-space limit. The functional ω ∆ ψ satisfies all the properties (2.23), thus establishing rigorously that the 1D bootstrap bound on the gap is 2∆ ψ + 1 for any ∆ ψ ∈ N. We were not able to find a closed form for the kernel defined by the sum (5.7).…”

“…The factor [v(ν)] ∆ ψ cancels the fast variation of ρ ∆ ψ (ν) with ν when ∆ ψ → ∞. The S-matrix for σ ≥ 4 can now be recovered through the formula 17) where the order of limits is important. In other words, S(µ 2 ) is simply the large ∆ ψ limit of the average value of e −iπ(∆ O −2∆ ψ ) over all primaries with ∆ O ∼ µ∆ ψ , weighted by (c ψψO /c free ψψO ) 2 .…”

Three-point functions at strong coupling in the BMN limit

“…An operatorial definition might facilitate the calculation of more general HHL form factors and shed light on the absence of wrapping advocated in this paper. It may also help filling the gap with the near-flat space limit [40,78,79]. One could perhaps reverse-engineer the formula obtained using integrability to reconstruct the worldsheet vertex.…”

Amplitudes on plane waves from ambitwistor strings

“…These worldsheet correlation functions reproduce the known results for 3-point scattering amplitudes of gravitons and gluons in gravitational and gauge theoretic plane wave backgrounds, respectively. 1 A notable special case where progress has been made is for AdS3, where the worldsheet theory is a SL(2, R) WZW model [27][28][29].2 It should be noted that worldsheet methods have been used to compute correlators in certain limits [34][35][36] or with special configurations of external states [37,38] in AdS backgrounds. Cubic string field theory has been used to study interactions on pp-wave backgrounds [39,40].…”

“…2 It should be noted that worldsheet methods have been used to compute correlators in certain limits [34][35][36] or with special configurations of external states [37,38] in AdS backgrounds. Cubic string field theory has been used to study interactions on pp-wave backgrounds [39,40].…”