Strings in the near plane wave background and AdS/CFT

TL;DR

The paper advances the AdS/CFT correspondence beyond the strict plane-wave limit by computing leading finite-radius (${\sim}{1/R^2}$) corrections to the plane-wave string spectrum in ${AdS}_5\times S^5$ and matching them to anomalous dimensions of refined BMN-like operators in planar ${\cal N}=4$ SYM. It develops a perturbative string analysis around the plane-wave background to obtain explicit corrections to the light-cone Hamiltonian, and constructs refined gauge-theory operators whose two-point functions yield a matrix ${\bf T}^{-1}{\bf F}$ that reproduces the string results. The key result is the exact matching of relevant matrix elements between the worldsheet string Hamiltonian and the gauge-theory dilatation operator at this order, supporting the robustness of the AdS/CFT correspondence near the Penrose limit. The work also outlines extensions to fermionic sectors, higher orders in ${1/R^2}$ and ${\lambda'}$, and broader backgrounds as avenues for future exploration.

Abstract

We study the AdS/CFT correspondence for string states which flow into plane wave states in the Penrose limit. Leading finite radius corrections to the string spectrum are compared with scaling dimensions of finite R-charge BMN-like operators. We find agreement between string and gauge theory results.

Figures (3)

• Figure 1: Order $g_{\rm Y\!M}^2$ corrections to scalar propagators consist of a gauge boson exchange and a fermion loop.
• Figure 2: Order $g_{\rm Y\!M}^2$ corrections to two point functions of operators of the form $\hbox{tr$\,$} z ... \phi^1 z ... \phi^2$: four-field irreducible blocks. When scalars $\phi^i$ are involved, the diagrams above represent the net contribution of all contributing Feynman diagrams, packaged in a way to mimic the $\cal N$=1 component fields Feynman diagrams. (Thick lines would correspond to exchanges of auxiliary fields $F_i$ and $D$ in the $\cal N$=1 formulation.) Diagrams with $z_2$ are given for comparison only. There are similar diagrams with one or both $z$-lines running in the opposite direction.
• Figure 3: Order $g^2$ corrections to two point functions of operators of the form $\hbox{tr$\,$} z ... \phi^1 z ... \phi^1$: four-field irreducible blocks. Thick lines correspond to exchanges if the gauge boson and auxiliary fields $F_i$ and $D$ in the $\cal N$=1 formulation. The diagrams above represent the net contribution of all contributing Feynman diagrams, packaged in a way to mimic the $\cal N$=1 component fields Feynman diagrams.