Reduced sigma-model on AdS_5 x S^5: one-loop scattering amplitudes

TL;DR

The work tests the quantum consistency of the Maldacena–Swanson near-flat-space truncation of the $AdS_5 \times S^5$ sigma-model by computing the one-loop $S$-matrix in the reduced theory and comparing it to the near-flat-space limit of the full string theory. It derives the reduced-model action in light-cone gauge, performs both tree-level and one-loop scattering of $Z$ and $Y$ fluctuations (with $\gamma=\pi/\sqrt{\lambda}$ and $m=1$), and finds a finite one-loop result. The imaginary and real parts of the one-loop amplitude reproduce exactly the corresponding pieces of the full theory after expansion in $1/\sqrt{\lambda}$, consistent with unitarity through the optical theorem. The results indicate decoupling of low-momentum modes in loops and suggest finiteness to all orders, validating the reduced model as a useful arena for testing the exact $S$-matrix and dressing phase in AdS/CFT.

Abstract

We compute one-loop S-matrix in the reduced sigma-model which describes AdS_5 x S^5 string theory in the near-flat-space limit. The result agrees with the corresponding limit of the S-matrix in the full sigma-model, which demonstrates the consistency of the reduction at the quantum level.

Figures (1)

• Figure 1: The scattering amplitude $ZY\rightarrow ZY$. Diagrams (b) and (c) contribute at tree level. The one-loop amplitude contains s-, t-, and u-channel diagram: (d), (e) and (f). Any of the fields $Z$, $Y$ and $\psi$ can propagate in the loop.