  We provide a non conformal generalization of the Comp\`ere-Song-Strominger
(CSS) boundary conditions for AdS$_3$ gravity that breaks the $\widehat u(1)$
Kac-Moody-Virasoro symmetry to two $u(1)$s. The holographic dual specified by
the new boundary conditions can be understood as an irrelevant deformation of a
warped conformal field theory (WCFT). Upon consistent reduction to two
dimensions, AdS$_3$ gravity results in a deformed Jackiw-Teitelboim dilaton
gravity model coupled to a Maxwell field. We show that near extremality the
boundary conditions inherited from generalized CSS boundary conditions in three
dimensions give rise to an effective action exhibiting the same symmetry
breaking pattern as the complex Sachdev-Ye-Kitaev models. Besides the
Schwarzian term reflecting the breaking of conformal symmetry, the effective
action contains an additional term that captures the breaking of the $\widehat
u(1)$ Kac-Moody symmetry.
