The geometry of large charge multi-traces in $$ \mathcal{N} $$ = 4 SYM

We construct a one-parameter family of half-BPS solutions of type IIB supergravity using a consistent truncation to gauged five-dimensional supergravity. For small values of the parameter, the solution reduces to the linear perturbation of AdS 5 × S 5 dual to the chiral primary operator in the stress-tensor multiplet, and we give evidence that the geometry is regular and asymptotes AdS in a normalisable way for arbitrarily large values of the parameter. We conjecture that the solution is the gravity dual of a “heavy” multi-trace operator in $$ \mathcal{N} $$ N = 4 SU( N ) Super Yang-Mills made by p copies of the stress-tensor chiral primary operator, with p of order N 2 in the large N limit. We perform some holographic checks supporting this duality map.