$\omega_1=0$ and $J_1,\bar J_1\rightarrow j_1$, this expression reduces to the regular term of (\[2pt\]).

Notice that a possible contact term in the two-point function of operators in the spectral flowed sector cannot be determined using this type of arguments. Indeed, such a term should only be relevant for $J_1\sim -1-J_2$, which would prevent us from setting both spin projections to extremal weights while attempting to use Eq. (\[identif33\]) as before.

Reflection symmetry in the winding sector {#sect5}
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A natural way to look for the contact term of the two-point function is by making use of the reflection symmetry, since, as we have already mentioned, a reflection operated in one vertex in the propagator would swap its contact and its regular terms. In this section we describe how such an operation can be defined for vertex operators with non-trivial spectral flow and in the space-time picture.

Eq. (\[reflembb\]) constitutes the naive extension of the reflection symmetry to spectral flowed sectors in the $m$-basis. We can read the effect of this symmetry in the $x$-basis by using, again, Eq. (\[identif33\]). By virtue of this equation, it follows from (\[reflembb\]) that $$\label{refletrucha}
\Phi^{j\omega}_{J}(\pm J|z) = Y^{-1-j,\omega}_{-1-J} \Phi^{-1-j,\omega}_{J}(\pm J|z).$$ The states appearing on 