Monodromies of CFT correlators on the Lorentzian cylinder

While correlators of a CFT are single valued in Euclidean Space, they are multi-valued - and have a complicated sheet structure - in Lorentzian space. Correlators on R^{1,1} R 1 , 1 are well known to access a finite number of these sheets. In this paper, we demonstrate the spiral nature of lightcones on $S^1 × $ time, which allows the time-ordered correlators of a CFT_2 C F T 2 on this spacetime - the Lorentzian cylinder - to access an infinite number of sheets of the correlator. We present a complete classification, both of the sheets accessed as well as of the various distinct causal configurations that lie on a particular sheet. Our construction provides a physical interpretation for an infinite number of sheets of the correlator, while, however, leaving a larger infinity of these sheets uninterpreted.