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Abstract In this work, we investigate holographic correlators of the stress tensor of a conformal field theory (CFT) on a torus within the context of AdS3 /CFT2. To compute the correlators of the stress tensor, we employ the Einstein-Hilbert theory of gravity and perturbatively solve Einstein’s equation in the bulk. In addition, we present an explicit prescription for developing a recurrence relation that simplifies the computation of higher point correlators. Our results show that the correlators and recurrence relation are consistent with known results in CFTs. Additionally, in line with the proposed cutoff-AdS/ T T ¯ $$ T\overline{T} $$ -CFT holography, we extend our computation program to investigate holographic torus correlators at a finite cutoff in the AdS3 and derive a parallel recurrence relation associated with higher point correlators.