Abstract
We compute the three-point structure constants for short primary operators of N=4 super Yang-Mills theory to leading order in the inverse coupling 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.
Highlights
A very satisfying result since the leading behavior was predicted well beforehand based on a flat-space approximation of a string on AdS5 × S5 [4]
The set of operators we considered are the chiral primaries as well as primaries which are dual to string states at the first massive level, which includes the Konishi operator
For short operators, the interaction region is small compared to the AdS radius, and the coupling at the intersection point is well approximated by a flat-space correlator of appropriate type IIB string vertex operators
Summary
We collect some relevant results from [21]. We assume that the operators are short operators in the sense that their sizes are much smaller than the AdS5 and S5 radii. It is convenient to shift the operator positions such that the intersection point is at xμ = 0 In this case all Mμν = 0 and the conserved charges Kiμ satisfy. These include the supergenerators Qαa and Qaα , where α and αare space-time spinor indices and a is an SO(6) spinor index (raised or lowered depending on which spinor representation), and the superconformal generators Sαa and Sαa We can put these into a form that is manifestly SU(2, 2) ≃ SO(2, 4) covariant by defining. Shifting the intersection point back to xμ = 0, the M−1μ are no longer zero, but the primary operator condition is still defined by the directions transverse. Where ΘA and ΘB are the sixteen-component left and right twist fields We only need these vertex operators in the (−1/2, −1/2) picture. Further technical details including a careful derivation of the supersymmetry transformations and the normalization factors can be found in appendix B.2
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
