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The two-dimensional $\mathcal{N}=4$ superconformal algebra has a free fieldrealization with four bosons and four fermions. There is an automorphism of thealgebra called spectral flow. Under spectral flow, the four fermions aretransformed together. In this paper, we study {\it partial spectral flow} whereonly two of the four fermions are transformed. Partial spectral flow is appliedto the D1D5 CFT where a marginal deformation moves the CFT away from the freepoint. The partial spectral flow is broken by the deformation. We show thatthis effect can be studied due to a transformation of the deformation which iswell-defined under partial spectral flow. As a result in the spectrum, wedemonstrate how to compute the second-order energy lift of D1D5P states fromtheir partial spectral flowed states. We find that D1D5P states related bypartial spectral flow do not have the same lift in general.

Partial Spectral Flow in the D1D5 CFT