Abstract
We explore and exploit the relation between non-planar correlators in mathcal{N} = 4 super-Yang-Mills, and higher-genus closed string amplitudes in type IIB string theory. By conformal field theory techniques we construct the genus-one, four-point string amplitude in AdS5 × S5 in the low-energy expansion, dual to an mathcal{N} = 4 super-Yang-Mills correlator in the ’t Hooft limit at order 1/c2 in a strong coupling expansion. In the flat space limit, this maps onto the genus-one, four-point scattering amplitude for type II closed strings in ten dimensions. Using this approach we reproduce several results obtained via string perturbation theory. We also demonstrate a novel mechanism to fix subleading terms in the flat space limit of AdS amplitudes by using string/M-theory.
Highlights
Four-particle amplitudes in type IIB string theory admit a double expansion: a genus expansion in different topologies in powers of gs, and a low energy expansion in powers of α
We explore and exploit the relation between non-planar correlators in N = 4 super-Yang-Mills, and higher-genus closed string amplitudes in type IIB string theory
We will focus on the four-point function O2O2O2O2 at O(1/c2) in the 1/λ expansion, and the matching of its flat space limit to the genus-one, four-point closed string amplitude in the α -expansion
Summary
Four-particle amplitudes in type IIB string theory admit a double expansion: a genus expansion in different topologies in powers of gs, and a low energy expansion in powers of α. We use our CFT methods to compute the functional form of certain discontinuities to all orders: first, any term in the α expansion of A(g=1) involving at least one R4 vertex; and second, the complete discontinuity of A(g=1) in the limit of forward scattering (t → 0) We independently derive these results, and determine the actual coefficients, using the string theory techniques of [25]. One of our main observations is that subleading terms in the s, t → ∞ limit of tree-level AdS Mellin amplitudes may be fixed by constructing the one-loop AdS amplitude, and matching its flat space limit to a one-loop string/M-theory amplitude. We end with a handful of open problems, while various appendices supplement the main text
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