Conformal Field Theory with Periodic Time

TL;DR

This paper demonstrates that 2D unitary conformal field theories can be extended to a Lorentzian torus with single-valued, conformally-invariant correlation functions when spatial and temporal radii are equal, under certain conditions.

Contribution

It establishes conditions under which Lorentzian CFT correlation functions extend to a conformally-invariant Lorentzian torus, generalizing previous results to higher dimensions.

Findings

Correlation functions extend to Lorentzian torus with equal radii.

Extension is conformally invariant and single-valued.

Results apply to higher-dimensional CFTs under null separation assumptions.

Abstract

It is shown that time-ordered correlation functions of a unitary CFT$_2$ in 2D Minkowski space admit a single-valued, conformally-invariant extension to the Lorentzian signature torus provided that the $S^1\times S^1$ spatial and temporal radii are equal. The result extends to Lorentzian CFT$_D$ on equal-radii $S^{D-1}\times S^1$ under the assumption that branch cuts occur only when a pair of operator insertions are null separated.