Scattering amplitudes in strongly coupled N=4 SYM from semiclassical strings in AdS

Abstract

Very recently in arXiv:0705.0303 Alday and Maldacena gave a string theory prescription for computing (all) planar amplitudes in N=4 supersymmetric gauge theory at strong coupling using the AdS/CFT correspondence. These amplitudes are determined by a classical string solution and contain a universal exponential factor involving the action of the classical string. On the gauge theory side, expressions for perturbative amplitudes at strong coupling were previously proposed only for specific helicities of external particles -- the maximally helicity violating or MHV amplitudes. These follow from the exponential ansatz of Bern, Dixon and Smirnov for MHV amplitudes in N=4 SYM. In this paper we examine the amplitudes dependence on helicities and particle-types of external states. We consider the prefactor of string amplitudes and give arguments suggesting that the prefactor at strong coupling should be the same as the Yang-Mills tree-level amplitude for the same process. This implies that scattering amplitudes in N=4 SYM simplify dramatically in the strong coupling limit. It follows from our proposal that in this limit all (MHV and non-MHV) n-point amplitudes are given by the (known) tree-level Yang-Mills result times the helicity-independent (and particle-type-independent) universal exponential.

Figures (5)

• Figure 1: Scattering of four open strings ending on $N$ coincident $D3$-branes. $A,B,C,D$ are the Chan-Paton indices labelling the branes on which strings end. For future reference we choose external states described by open strings with one end on the $N^{\rm th}$ brane, $B=D=N$ (shown in blue), and the other end on the remaining $N-1$ branes, $A,C=1,\ldots N-1$ (shown in red).
• Figure 2: Scattering of open strings stretched between the separated IR brane and the stack of $N-1$$D3$-branes.
• Figure 3: In the Maldacena near-horizon limit the $N-1$ stack dissolves into the $AdS_5 \times S^5$ geometry and the IR brane is the only brane remaining. The stretched strings worldsheet in Figure 2 becomes the open string worldsheet curved into the $AdS$ bulk. We show a slice of this worldsheet at finite values of $X^\mu$. In the asymptotic region $X^\mu \to \infty$ the red dotted lines approach the IR brane so that all the asymptotic scattering states are located on the IR brane.
• Figure 4: Four point scattering in the T-dual picture (with sides rescaled from $\sqrt{s}/4$ to unity.
• Figure 5: $(y_1,y_2)$-projection of the solution for four-point scattering showing the square boundary, and the smoothed boundary. The shaded inner region (in grey) shows the IR regulated "bulk" contribution. The dotted outer region is where the patched solution is constructed with $r \simeq r_{IR}$.