We formulate a renormalization theory for irrelevant perturbations to the IR fixed point in the SYK model. By integrating out the lowest resonance in the four-point function of the microscopic fermion, we derive a non-local action for the reparametrization mode. We propose a gravity dual with matter fields in addition to the dilaton which imposes conformal gauge on the metric. This gravity theory reproduces the non-local action of the SYK model on its boundary.