Huge BPS operators and fluid dynamics in $$ \mathcal{N}=4 $$ SYM

A bstract In the bulk dual of holography, huge operators correspond to sources so heavy that they fully backreact on the space-time geometry. Here we study the correlation function of three such huge operators when they are given by 1 / 2 BPS operators in $$ \mathcal{N}=4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:math> SYM theory, dual to IIB Strings in AdS 5 × S 5 . We unveil simple matrix model representations for these correlators which we can sometimes solve analytically. For general huge operators, we translate these matrix model expressions into a 1 + 1 dimensional hydrodynamical fluid problem. This fluid is integrable thus unveiling a novel integrable sector of the AdS/CFT duality in a full fledged gravitational regime, very far from the usual free string planar regime where integrability reigns supreme. We explain how an adiabatic deformation method can be developed to yield the solution to an integrable discrete formulation of these fluids — the rational Calogero-Moser Model — so we can access the general three point correlation functions of generic huge 1 / 2-BPS operators. Everything will be done on the gauge theory side of the duality. It would be fascinating to find the holographic dual of these matrix models and fluids.