The quartic effective action for Kaluza-Klein modes that arises upon compactification of type IIB supergravity on the five-sphere S 5 is a starting point for computing the four-point correlation functions of arbitrary weight 1 2 -BPS operators in N = 4 super Yang-Mills theory in the supergravity approximation. The apparent structure of this action is rather involved, in particular it contains quartic terms with four derivatives which cannot be removed by field redefinitions. By exhibiting intricate identities between certain integrals involving spherical harmonics of S 5 we show that the net contribution of these four-derivative terms to the effective action vanishes. Our result is in agreement with and provides further support to the recent conjecture on the Mellin space representation of the four-point correlation function of any 1 2 -BPS operators in the supergravity approximation.

We present the computation of all the correlators of 1/2-BPS operators in N = 4 SYM with weights up to 8 as well as some very high-weight correlation functions from the effective supergravity action. The computation is done by implementing the recently developed simplified algorithm in combination with the harmonic polynomial formalism. We provide a database of these results attached to this publication and additionally check for almost all of the functions in this database that they agree with the conjecture on their Mellin-space form.

Recently a Mellin-space formula was conjectured for the form of correlation functions of 1/2 BPS operators in planar N = 4 SYM in the strong 't Hooft coupling limit. In this work we report on the computation of two previously unknown four-point functions of operators with weights 2345 and 3456 , from the effective type-IIB supergravity action using AdS/CFT. These correlators are novel: they are the first correlators with all different weights and in particular 3456 is the first next-next-next-to-extremal correlator to ever have been computed. We also present simplifications of the known algorithm, without which these computations could not have been executed. These simplifications consist of a direct formula for the exchange part and for the contact part of the correlation function, as well as a simplification of the C tensor algorithm to compute a tensors. After bringing our results in the appropriate form we successfully corroborate the recently conjectured formula.

We consider the half-wave maps (HWM) equation which provides a continuum description of the classical Haldane–Shastry spin chain on the real line. We present exact multi-soliton solutions of this equation. Our solutions describe solitary spin excitations that can move with different velocities and interact in a non-trivial way. We make an ansatz for the solution allowing for an arbitrary number of solitons, each described by a pole in the complex plane and a complex spin variable, and we show that the HWM equation is satisfied if these poles and spins evolve according to the dynamics of an exactly solvable spin Calogero–Moser (CM) system with certain constraints on initial conditions. We also find first order equations providing a Bäcklund transformation of this spin CM system, generalize our results to the periodic HWM equation, and provide plots that visualize our soliton solutions.