Singularities of thermal correlators at strong coupling

We analyze the singularities of the two-point function in a conformal field theory at finite temperature. In a free theory, the only singularity is along the boundary light cone. In the holographic limit, a new class of singularities emerges since two boundary points can be connected by a nontrivial null geodesic in the bulk, encircling the photon sphere of the black hole. We show that these new singularities are resolved by tidal effects due to the black hole curvature, by solving the string world sheet theory in the Penrose limit. Singularities in the asymptotically flat black hole geometry are also discussed.

Figure 1

The locations of the singularities on the boundary. The top figure is for small masses, $4M\sim 0.2$, and the bottom figure is for larger masses, $4M\sim 2$. The angle $\varphi$ has period $2\pi$, and the dashed lines are identified with each other. The standard light cone is in red, and the new singularities are in blue.

Figure 2

The intersection pattern of the singularity curves. We see that the number of curves intersecting a given time slice grows linearly with time. Whenever two curves intersect, there is a caustic.

Figure 3

The light cone in the asymptotically flat case is a single smooth curve. Here we set $r_s/r_{\max }=1/10$.