Dressing phases of AdS3/CFT2

TL;DR

This work determines the all-loop dressing phases for the AdS3/CFT2 integrable system with RR flux by solving the crossing relations on the rapidity torus. The authors construct two distinct phases derived from BES and HL building blocks, ensuring correct strong-coupling limits (AFS universality at leading order; HL differences at subleading order), and analyze their bound-state structure through pole analysis of the S-matrix. They provide explicit strong-, semiclassical/near-flat-space, and weak-coupling expansions, revealing novel features such as r=1 contributions in the AdS3 case and highlighting consistency with known perturbative results while noting subtle discrepancies that demand further checks. The results establish a nonperturbative dressing-factor framework for AdS3/CFT2 and lay groundwork for incorporating massless modes and higher-loop perturbative tests.

Abstract

We determine the all-loop dressing phases of the AdS3/CFT2 integrable system related to type IIB string theory on AdS3 x S3 x T4 by solving the recently found crossing relations and studying their singularity structure. The two resulting phases present a novel structure with respect to the ones appearing in AdS5/CFT4 and AdS4/CFT3. In the strongly-coupled regime, their leading order reduces to the universal Arutyunov-Frolov-Staudacher phase as expected. We also compute their sub-leading order and compare it with recent one-loop perturbative results, and comment on their weak-coupling expansion.

Figures (4)

• Figure 1: The rapidity torus with several significant curves. The solid blue line is the real $z$-axis (physical region), the dashed blue line is the $z=\omega_2$ axis ("crossed" region). In the leftmost figure the torus is divided in four regions by $|x^\pm|=1$ and in the central figure it is divided by $\mathop{\operatorname{Im}}(x^\pm)=0$. The rightmost picture depicts both sets of curves, which intersect in eight points with real part $\pm\omega_1/4$.
• Figure 2:
• Figure 3: On the left two particles in the same sector form an $\mathfrak{su}(2)$ bound state in the $s$-channel. Applying the crossing transformation to $\Phi_p^{+\dot{+}}$ yields the $t$-channel diagram on the right, where on particle has unphysical momentum $\bar{p}$ (red dashed lines). Particles are labeled as in Borsato:2013qpa.
• Figure 4: On the left the would-be Landau diagram for one left- and one right-moving particle is depicted. This process should be absent. Similarly, the crossed process on the right should be absent, and the corresponding S-matrix element have no pole.