Spinning geodesic Witten diagrams

Abstract:We revisit the so-called "Geodesic Witten Diagrams" (GWDs) [1], proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.

Section: Jhep05(2017)070supporting

confidence: 64%

Section: Jhep05(2017)070mentioning

confidence: 99%

Anatomy of geodesic Witten diagrams

Chen

Kuo

Kyono

2017

“…17 Further generalizations to spinning external and exchanged operators were considered in Refs. [83,84,85,86,72,87,88,89,90]. It is helpful to consider an alternate representation of (4.1), which makes the comparison with the higherpoint blocks discussed below more transparent.…”

Section: ĝĝĝmentioning

confidence: 99%

“…[62,94,93,97,98,99,96,101,102]). In arbitrary spacetime dimensions, it is also natural to consider the generalizations of the holographic duals of the higher-point scalar blocks of this paper to those involving external and exchanged spinning operators, along the lines of the four-point case [83,84,85,86,88,89,90]. Progress along this direction may also aid the technically challenging task of the holographic reconstruction of the classical bulk action for higher spin gravity theories beyond quartic interaction vertices [128,129,130].…”

Section: Spectral Decomposition Of Ads Diagramsmentioning

confidence: 99%

Propagator identities, holographic conformal blocks, and higher-point AdS diagrams

Jepsen

Parikh

2019

Conformal blocks are the fundamental, theory-independent building blocks in any CFT, so it is important to understand their holographic representation in the context of AdS/CFT. We describe how to systematically extract the holographic objects which compute higherpoint global (scalar) conformal blocks in arbitrary spacetime dimensions, extending the result for the four-point block, known in the literature as a geodesic Witten diagram, to five-and six-point blocks. The main new tools which allow us to obtain such representations are various higher-point propagator identities, which can be interpreted as generalizations of the well-known flat space star-triangle identity, and which compute integrals over products of three bulk-to-bulk and/or bulk-to-boundary propagators in negatively curved spacetime. Using the holographic representation of the higher-point conformal blocks and higher-point propagator identities, we develop geodesic diagram techniques to obtain the explicit directchannel conformal block decomposition of a broad class of higher-point AdS diagrams in a scalar effective bulk theory, with closed-form expressions for the decomposition coefficients. These methods require only certain elementary manipulations and no bulk integration, and furthermore provide quite trivially a simple algebraic origin of the logarithmic singularities of higher-point tree-level AdS diagrams. We also provide a more compact repackaging in terms of the spectral decomposition of the same diagrams, as well as an independent discussion on the closely related but computationally simpler framework over p-adics which admits comparable statements for all previously mentioned results.

“…8 Here is another intuitive explanation. In perturbation theory, the double-trace operators require computing the full Witten diagram for the four-point function, whereas the contributions from an exchanged operator require computing only the Witten diagram where the bulk-to-boundary propagators are integrated over geodesics [19,[35][36][37]. This result has been demonstrated for single-trace operator exchange in general d and for semiclassical gravity in d = 2.…”

Section: Introductionmentioning

confidence: 99%

Universal lowest-twist in CFTs from holography

Fitzpatrick

Huang

2019

179

We probe the conformal block structure of a scalar four-point function in d ≥ 2 conformal field theories by including higher-order derivative terms in a bulk gravitational action. We consider a heavy-light four-point function as the boundary correlator at large central charge. Such a four-point function can be computed, on the gravity side, as a two-point function of the light operator in a black hole geometry created by the heavy operator. We consider analytically solving the corresponding scalar field equation in a near-boundary expansion and find that the multi-stress tensor conformal blocks are insensitive to the horizon boundary condition. The main result of this paper is that the lowest-twist operator product expansion (OPE) coefficients of the multi-stress tensor conformal blocks are universal: they are fixed by the dimension of the light operators and the ratio between the dimension of the heavy operator and the central charge C T . Neither supersymmetry nor unitary is assumed. Highertwist coefficients, on the other hand, generally are not protected. A recursion relation allows us to efficiently compute universal lowest-twist coefficients. The universality result hints at the potential existence of a higher-dimensional Virasoro-like symmetry near the lightcone. While we largely focus on the planar black hole limit in this paper, we include some preliminary analysis of the spherical black hole case in an appendix.Aside from making the expressions more compact, the variable σ defined above is convenient since it parameterizes the angle away from the lightcone of the path made when one varies 32 This fact is obvious for n = 0, since Q 0 (w) = 1. Taking Q 2n (w) ∼ w γn at small w, the field equation requires γ n = γ n−1 − 2 for the contributions from subsequent Q 2n (w)s to cancel against each other.33 In our convention, a n,n = (−4) J 2 c OPE (τ min , J) in d = 4.