The AdS Veneziano amplitude at small curvature

Abstract

We compute the AdS Veneziano amplitude for type IIB gluon scattering in $AdS_5 \times S^3$ to all orders in $α'$ in a small curvature expansion. This is achieved by combining a dispersion relation in the dual $4d$ $\mathcal{N}=2$ SCFT with an ansatz for the amplitude as a worldsheet integral in terms of multiple polylogarithms. The first curvature correction is fully fixed in this way and satisfies consistency checks in the high energy limit, the low energy expansion as previously fixed using supersymmetric localisation, and for the energy of massive string operators, which we independently compute using a semiclassical expansion. We also combine localisation with this first curvature correction to fix the unprotected $D^4F^4$ correction to the amplitude at finite curvature.

Figures (7)

• Figure 1: Chew-Frautschi plot of the spectrum of operators exchanged in the Veneziano amplitude.
• Figure 2: Illustration of the closed mixed folded string solution. The solution contains four identical segments, which are split in the plot for clarity. The four segments correspond to $\sigma$ in the intervals $[0, \pi/2]$, $[\pi/2, \pi]$, $[\pi, 3\pi/2]$, and $[3\pi/2, 2\pi]$, respectively, and are coloured in red, cyan, violet, and purple for visual distinction.
• Figure 3: Illustration of the closed folded $S^5$ string solution. The solution contains four identical segments, which are split in the plot for clarity. The four segments correspond to $\sigma$ in the intervals $[0, \pi/2]$, $[\pi/2, \pi]$, $[\pi, 3\pi/2]$, and $[3\pi/2, 2\pi]$, respectively, and are coloured in red, cyan, violet, and purple for visual distinction.
• Figure 4: Open folded string solution from closed folded string solution: we take half of the solution and relabel the coordinate by $\sigma \rightarrow \sigma - \pi/2$.
• Figure 5: Open folded string solution from closed folded string solution: we take half of the solution and relabel the coordinate by $\sigma \rightarrow \sigma - \pi/2$.