Late time Wilson lines

TL;DR

This paper uses Wilson line techniques to analyze Virasoro conformal blocks at large central charge in the late-time regime, revealing decay, erratic behavior, and recurrences, and connects these to gravitational effects on operator dimensions.

Contribution

It derives new analytical results on late-time Virasoro blocks in AdS$_3$/CFT$_2$ using Wilson lines, focusing on light-light blocks and their time dependence.

Findings

Conformal blocks exhibit initial decay and subsequent erratic behavior.

Resummation of time dependence in large c regime.

Connection between conformal blocks and gravitational anomalous dimensions.

Abstract

In the AdS$_3$/CFT$_2$ correspondence, physical interest attaches to understanding Virasoro conformal blocks at large central charge and in a kinematical regime of large Lorentzian time separation, $t\sim c$. However, almost no analytical information about this regime is presently available. By employing the Wilson line representation we derive new results on conformal blocks at late times, effectively resumming all dependence on $t/c$. This is achieved in the context of "light-light" blocks, as opposed to the richer, but much less tractable, "heavy-light" blocks. The results exhibit an initial decay, followed by erratic behavior and recurrences. We also connect this result to gravitational contributions to anomalous dimensions of double trace operators by using the Lorentzian inversion formula to extract the latter. Inverting the stress tensor block provides a pedagogical example of inversion formula machinery.