Worldsheet spectrum in AdS(4)/CFT(3) correspondence

TL;DR

The paper resolves a degree-of-freedom mismatch in the AdS$_4$/CFT$_3$ integrable system by showing that heavy BMN modes dissolve into the light-mode continuum when $\alpha'$ corrections are included. Using a near-BMN expansion of the AdS$_4\times CP^3$ worldsheet sigma-model in light-cone gauge, it computes the one-loop polarization of a heavy mode and the tree-level scattering of light modes, demonstrating that the heavy pole disappears and the S-matrix remains reflectionless. The tree-level worldsheet amplitudes precisely match the strong-coupling expansion of the conjectured exact S-matrix based on Beisert PSU(2|2) with a dressing phase, including the necessary heavy-mode contributions. This supports the view that the physical worldsheet spectrum consists of the 4 bosonic and 4 fermionic light modes, with heavy modes contributing as intermediate states in perturbation theory and aligning with the spin-chain description of the dual Chern-Simons theory.

Abstract

The AdS(4)/CFT(3) duality is a new example of an integrable and exactly solvable AdS/CFT system. There is, however, a puzzling mismatch between the number of degrees of freedom used in the exact solution (4B+4F scattering states) and 8B+8F transverse oscillation modes of critical superstring theory. We offer a resolution of this puzzle by arguing that half of the string modes dissolve in the continuum of two-particle states once alpha' corrections are taken into account. We also check that the conjectured exact S-matrix of AdS(4)/CFT(3) agrees with the tree-level worldsheet calculation.

Figures (2)

• Figure 1: The one-loop self-energy graphs.
• Figure 2: The scattering ($XX\rightarrow XX$), transmission ($X\bar{X}\rightarrow X\bar{X}$) and reflection ($X\bar{X}\rightarrow \bar{X}X$) amplitudes. At tree level, they are given by the sum of the contact interaction diagram (c) and the exchange graphs with the heavy mode $Z$ in the (s), (t), and (u) channels.