SciPost Phys. 19, 162 (2025) ·
published 23 December 2025
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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 $R^{1,1}$ 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 $CFT_2$ 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.
