Holographic conformal blocks from interacting Wilson lines

Abstract

We present a simple prescription for computing conformal blocks and correlation functions holographically in AdS$_3$ in terms of Wilson lines merging at a bulk vertex. This is shown to reproduce global conformal blocks and heavy-light Virasoro blocks. In the case of higher spin theories the space of vertices is in one-to-one correspondence with the space of ${\cal W}_N$ conformal blocks, and we show how the latter are obtained by explicit computations.Comment: 40 pages, 1 figur

On information loss in AdS3/CFT2

“…Were this the case, our task would be hopeless, since we will not be able to compute the exact heavy-light correlator in any, let alone every, holographic CFT. Fortunately, in all CFT 2 there is a universal contribution to each heavy-light correlator, the Virasoro vacuum block [20][21][22][23][24][25][26][27][28], which manifests information loss in the large central charge or c → ∞ limit [29].…”

“…However, we also obtain contributions from the O (5,1) state as z fully encircles 1. The other case has a fusion rule 28) which is of interest because in the large c limit it contains both the heavy states O (3,1) and O (3,3) , whose dimensions grow with c, and the light state O (1,3) , which has a fixed dimension as c → ∞. However, in our preliminary work we have not found a clean separation between effects from the light and heavy states, as all critical points of the I (2,2) action appear to coalesce in the neighborhood of the forbidden singulairty.…”

Degenerate operators and the 1/c expansion: Lorentzian resummations, high order computations, and super-Virasoro blocks

“…The reason is that correlation functions in any CFT 2 can be decomposed into Virasoro conformal blocks V h i ,h,c (z) The Virasoro blocks have turned out to be extremely useful as a source of information about gravity in AdS 3 , and in fact BTZ black hole [4] thermodynamics [5] emerges in a universal, theory-independent way from the heavy-light, large central charge limit of the Virasoro blocks [6][7][8][9][10][11][12][13][14][15]. Information loss from black hole physics appears to be due to the behavior of the blocks in this limit [3,7,11].…”

Holographic interpretation of 1-point toroidal block in the semiclassical limit

“…Simons formulation [33,34], for recent discussion see, e.g., [35][36][37][38]. Finally, it is interesting to develop the geodesic Witten diagrams technique by analogy with conformal blocks on the complex plane [10].…”