Renormalization of gravitational Wilson lines

First-quantized propagation in quantum gravitational AdS 3 backgrounds can be exactly reconstructed using CFT 2 data and Virasoro symmetry. We develop methods to compute the bulk-to-boundary propagator in a black hole microstate, φ L O L O H O H , at finite central charge. As a first application, we show that the semiclassical theory on the Euclidean BTZ solution sharply disagrees with the exact description, as expected based on the resolution of forbidden thermal singularities, though this effect may appear exponentially small for physical observers. arXiv:1810.02436v2 [hep-th] 30 Apr 2019 1 By the Planck scale we mean an energy scale c 24 ; the details won't be important for this informal discussion. We do not know if a CFT like this actually exists, nor do we know of any bottom-up constraints that make the existence of such a CFT appear problematic.2 Graviton exchanges in n + 1-pt correlators induce mixing between ϕ and n-particle states, so that ϕO n = 0, whereas φ has a vanishing 2-pt function with multi-trace operators. We describe this in more detail in appendix D.10 For a nice pedagogical introduction to the monodromy method, see appendix D of [54]. 11 This holomorphic bulk block can be obtained by taking a chiral limit where c R c L and in particular c R is infinitely larger than all the other parameters that determine the correlator, so that the right-moving stress tensors decouple; it can therefore be thought of as a chiral gravity limit.

Section: Discussionmentioning

confidence: 99%

The bulk-to-boundary propagator in black hole microstate backgrounds

Chen¹,

Fitzpatrick²,

Kaplan³

et al. 2019

“…To begin, it would be nice to perform bulk calculations that match the 1/c expansion of the anomalous twist (1.8) for light external operators (e.g. using Wilson lines [16,[47][48][49][50] or proto-fields [51]). Likewise, the effective theory in [52] may also be capable of reproducing our results.…”

Section: Late Timementioning

confidence: 99%

Quantum Regge trajectories and the Virasoro analytic bootstrap

Collier

Gobeil

Maxfield

et al. 2019

201

Every conformal field theory (CFT) above two dimensions contains an infinite set of Regge trajectories of local operators which, at large spin, asymptote to "double-twist" composites with vanishing anomalous dimension. In two dimensions, due to the existence of local conformal symmetry, this and other central results of the conformal bootstrap do not apply. We incorporate exact stress tensor dynamics into the CFT 2 analytic bootstrap, and extract several implications for AdS 3 quantum gravity. Our main tool is the Virasoro fusion kernel, which we newly analyze and interpret in the bootstrap context. The contribution to double-twist data from the Virasoro vacuum module defines a "Virasoro Mean Field Theory" (VMFT); its spectrum includes a finite number of discrete Regge trajectories, whose dimensions obey a simple formula exact in the central charge c and external operator dimensions. We then show that VMFT provides a baseline for large spin universality in two dimensions: in every unitary compact CFT 2 with c > 1 and a twist gap above the vacuum, the double-twist data approaches that of VMFT at large spin . Corrections to the large spin spectrum from individual non-vacuum primaries are exponentially small in √ for fixed c. We analyze our results in various large c limits. Further applications include a derivation of the late-time behavior of Virasoro blocks at generic c; a refined understanding and new derivation of heavy-light blocks; and the determination of the cross-channel limit of generic Virasoro blocks. We deduce non-perturbative results about the bound state spectrum and dynamics of quantum gravity in AdS 3 .

“…This is achieved in a perturbative expansion of the geometric action on the BMS 3 coadjoint orbits. The same techniques will be applied in the next section to compute the BMS 3 identity block, both for light operators and in the heavy-light limit, but first we will compute the Wilson line (5.5), generalizing to flat space the construction of [102,103].…”

Section: Wilson Lines and Entanglement Entropymentioning

confidence: 99%

“…In line with the AdS 3 computation of the Wilson line in [102,103] we take the following choice of in-and out-state in a highest-weight representations of isl(2, R)…”

Section: Bilocal Operators From Wilson Linesmentioning

confidence: 99%

Geometric actions and flat space holography

Merbis

Riegler²

2020

In this paper we perform the Hamiltonian reduction of the action for three-dimensional Einstein gravity with vanishing cosmological constant using the Chern-Simons formulation and Bondi-van der Burg-Metzner-Sachs (BMS) boundary conditions. An equivalent formulation of the boundary action is the geometric action on BMS 3 coadjoint orbits, where the orbit representative is identified as the bulk holonomy. We use this reduced action to compute one-loop contributions to the torus partition function of all BMS 3 descendants of Minkowski spacetime and cosmological solutions in flat space. We then consider Wilson lines in the ISO(2, 1) Chern-Simons theory with endpoints on the boundary, whose reduction to the boundary theory gives a bilocal operator. We use the expectation values and two-point correlation functions of these bilocal operators to compute quantum contributions to the entanglement entropy of a single interval for BMS 3 invariant field theories and BMS 3 blocks, respectively. While semi-classically the BMS 3 boundary theory has central charges c 1 = 0 and c 2 = 3/G N , we find that quantum corrections in flat space do not renormalize G N , but rather lead to a non-zero c 1 .