Witten diagrams revisited: the AdS geometry of conformal blocks

By E. Hijano, Per Kraus, Eric Perlmutter, River Snively. 2015

299 citations recorded by the source corpus.

A bstractWe develop a new method for decomposing Witten diagrams into conformal blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly simple answer to the question: what object in AdS computes a conformal block? The answer is a “geodesic Witten diagram”, which is essentially an ordinary exchange Witten diagram, except that the cubic vertices are not integrated over all of AdS, but only over bulk geodesics connecting the boundary operators. In particular, we consider the case of four-point functions of scalar operators, and show how to easily reproduce existing results for the relevant conformal blocks in arbitrary dimension.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a2daab01557540a078b8d42bccd469e1be5eae63

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Citations in the corpus

Bounding the space of holographic CFTs with chaos (2016, methodology): “One way to understand why G ∆,s ∼ z1−s is that conformal blocks G∆,s in CFTd are equivalent to geodesic Witten diagrams in AdSd+1 for spin-s exchange [82].”
Loops in AdS from conformal field theory (2016, background): “Even at tree-level, the original calculations [4–13] were impressive but arduous, and struggled to make manifest the relation to CFT data; only recently have leaner, more transparent methods been introduced, including Mellin space [14, 15] and geodesic Witten diagrams [16].”
Semiclassical Virasoro blocks from AdS3 gravity (2015, methodology): “To This field solution was denoted φ ∆ (y ′) in [1].”
A stereoscopic look into the bulk (2016, methodology): “In this paper we discussed the modular Hamiltonian and its behavior in kinematic space [11] as well as the holographic representation of conformal blocks in terms of geodesic Witten diagrams [21, 22].”
A Mellin space approach to the conformal bootstrap (2016, methodology): “We also thank all our other (28)There is a geometric way of understanding the conventional conformal blocks in terms of geodesic Witten diagrams [62].”
Quartic AdS interactions in higher-spin gravity from Conformal Field Theory (2015, background): “Such an object was recently defined in [69].”