However, these selection rules state that the two-point function must necessarily preserve the total spectral flow charge. Since different assignments of spectral flow adding up to the same amount only affect the overall worldsheet dependence of correlators, it follows that $$\label{2ptsl2bb}
\left\langle\Phi^{\omega_1}_{j_1}(m_1|z_1)\Phi^{\omega_2}_{j_2}(m_2|z_2)\right\rangle=\delta_{\omega_1+\omega_2,0}\delta^2(m_1+m_2)\left[\delta\left(j_{12}^+\right)+Y^{-1-j_1}_{m_1}\delta\left(j_{12}\right)\right]\left|z_{12}^{-2\Delta_1}\right|^2.$$

Importantly, the reflection symmetry extends to the spectral flowed sector as $$\label{reflembb}
\Phi^{\omega}_j(m|z)=Y^{-1-j}_{m}\Phi^{\omega}_{-1-j}(m|z).$$ We will make extensive use of this property below.

Winding modes in the space-time picture {#sect4}
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As we have already pointed out, the $m$-basis is convenient for introducing spectral flow charges. However, the space-time picture is the best suited for interpreting any result in the context of the AdS/CFT conjecture since the $x$-basis vertex operators are ingredients for the string theory operators describing states created by sources in the boundary of the target space. Indeed, if $\Theta(z)$ is a spinless worldsheet vertex corresponding to the internal CFT, the operator $$V_{j}(x)\sim \int_{\mathbb C} d^2z \, \Phi_j(x|z) \Theta(z)\nonumber$$ can be realized (as long as the scaling dimension of the full vertex equals one) as describing a string state created by a point-like source located at $x$ on the boundary of AdS$_3$. By means of the AdS/CFT correspondence, it can be identified with a CFT operator inserted 