Bootstrapping string theory on AdS$_5 \times S^5$

Understand

We make an ansatz for the Mellin representation of the four-point amplitude of half-BPS operators of arbitrary charges at order $\lambda^{-\frac{5}{2}}$ in an expansion around the supergravity limit.

• Crossing symmetry and a set of constraints on the form of the spectrum uniquely fix the amplitude and double-trace anomalous dimensions at this order.
• The results exhibit a number of natural patterns which suggest that the bootstrap approach outlined here will extend to higher orders in a simple way.