Genus-One String Amplitudes from Conformal Field Theory

TL;DR

This paper constructs genus-one four-point string amplitudes in AdS$_5\times S^5$ using conformal field theory, connecting AdS correlators with flat space string scattering, and reproduces known results while introducing a new method to determine subleading terms.

Contribution

It develops a CFT-based method to compute genus-one string amplitudes in AdS and flat space, providing a novel way to fix subleading terms using string/M-theory insights.

Findings

Constructed genus-one four-point amplitudes in AdS$_5\times S^5$

Mapped AdS amplitudes to flat space string scattering

Reproduced known string perturbation results and fixed subleading terms

Abstract

We explore and exploit the relation between non-planar correlators in ${\cal N}=4$ 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 AdS$_5\times S^5$ in the low-energy expansion, dual to an ${\cal N}=4$ super-Yang-Mills correlator in the 't Hooft limit at order $1/c^2$ 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.