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Abstract We combine old and new quantum field theoretic arguments to show that any theory of stable or metastable higher spin particles can be coupled to gravity only when the gravity sector has a stringy structure. Metastable higher spin particles, free or interacting, cannot couple to gravity while preserving causality unless there exist higher spin states in the gravitational sector much below the Planck scale M pl. We obtain an upper bound on the mass Λgr of the lightest higher spin particle in the gravity sector in terms of quantities in the non-gravitational sector. We invoke the CKSZ uniqueness theorem to argue that any weakly coupled UV completion of such a theory must have a gravity sector containing infinite towers of asymptotically parallel, equispaced, and linear Regge trajectories. Consequently, gravitational four-point scattering amplitudes must coincide with the closed string four-point amplitude for s, t ≫ 1, identifying Λgr as the string scale. Our bound also implies that all metastable higher spin particles in 4d with masses m ≪ Λgr must satisfy a weak gravity condition.

Abstract Causality constrains the gravitational interactions of massive higher spin particles in both AdS and flat spacetime. We explore the extent to which these constraints apply to composite particles, explaining why they do not rule out macroscopic objects or hydrogen atoms. However, we find that they do apply to glueballs and mesons in confining large N gauge theories. Assuming such theories contain massive bound states of general spin, we find parametric bounds in (3 + 1) spacetime dimensions of the form N ≲ M Pl Λ QCD $$ N\lesssim \frac{M_{Pl}}{\Lambda_{\mathrm{QCD}}} $$ relating N, the QCD scale, and the Planck scale. We also argue that a stronger bound replacing ∧QCD with the UV cut-off scale may be derived from eikonal scattering in flat spacetime.

Abstract The gauge redundancy of quantum gravity makes the definition of local operators ambiguous, as they depend on the choice of gauge or on a ‘gravitational dressing’ analogous to a choice of Wilson line attachments. Recent work identified exact AdS3 proto-fields by fixing to a Fefferman-Graham gauge. Here we extend that work and define proto-fields with general gravitational dressing. We first study bulk fields charged under a U(1) Chern-Simons gauge theory as an illustrative warm-up, and then generalize the results to gravity. As an application, we compute a gravitational loop correction to the bulk-boundary correlator in the background of a black hole microstate, and then verify this calculation using a newly adapted recursion relation. Branch points at the Euclidean horizon are present in the 1/c corrections to semiclassical correlators.

Abstract First-quantized propagation in quantum gravitational AdS3 backgrounds can be exactly reconstructed using CFT2 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 $$ \left\langle {\phi}_L{\mathcal{O}}_L{\mathcal{O}}_H{\mathcal{O}}_H\right\rangle $$ , 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.

Abstract We present a prescription for an effective lightcone (LC) Hamiltonian that includes the effects of zero modes, focusing on the case of Conformal Field Theories (CFTs) deformed by relevant operators. We show how the prescription resolves a number of issues with LC quantization, including i) the apparent non-renormalization of the vacuum, ii) discrepancies in critical values of bare parameters in equal-time vs LC quantization, and iii) an inconsistency at large N in CFTs with simple AdS duals. We describe how LC quantization can drastically simplify Hamiltonian truncation methods applied to some large N CFTs, and discuss how the prescription identifies theories where these simplifications occur. We demonstrate and check our prescription in a number of examples.

Abstract We recently used Virasoro symmetry considerations to propose an exact formula for a bulk proto-field ϕ in AdS3. In this paper we study the propagator 〈ϕϕ〉. We show that many techniques from the study of conformal blocks can be generalized to compute it, including the semiclassical monodromy method and both forms of the Zamolodchikov recursion relations. When the results from recursion are expanded at large central charge, they match gravitational perturbation theory for a free scalar field coupled to gravity in our chosen gauge. We find that although the propagator is finite and well-defined at long distances, its perturbative expansion in GN=32c $$ {G}_N=\frac{3}{2c} $$ exhibits UV/IR mixing effects. If we nevertheless interpret 〈ϕϕ〉 as a probe of bulk locality, then when GNmϕ≪1 $$ {G}_{N{m}_{\phi }}\ll 1 $$ locality breaks down at the new short-distance scale σ∗∼GNRAdS34 $$ {\sigma}_{\ast}\sim \sqrt[4]{G_N{R}_{\mathrm{AdS}}^3} $$. For ϕ with very large bulk mass, or at small central charge, bulk locality fails at the AdS length scale. In all cases, locality ‘breakdown’ manifests as singularities or branch cuts at spacelike separation arising from non-perturbative quantum gravitational effects.

Abstract We use conformal symmetry to define an AdS3 proto-field ϕ as an exact linear combination of Virasoro descendants of a CFT2 primary operator O $$ \mathcal{O} $$. We find that both symmetry considerations and a gravitational Wilson line formalism lead to the same results. The operator ϕ has many desirable properties; in particular it has correlators that agree with gravitational perturbation theory when expanded at large c, and that automatically take the correct form in all vacuum AdS3 geometries, including BTZ black hole backgrounds. In the future it should be possible to use ϕ to probe bulk locality and black hole horizons at a non-perturbative level.

Abstract We chart the breakdown of semiclassical gravity by analyzing the Virasoro conformal blocks to high numerical precision, focusing on the heavy-light limit correspond-ing to a light probe propagating in a BTZ black hole background. In the Lorentzian regime, we find empirically that the initial exponential time-dependence of the blocks transitions to a universal t − 3 2 $$ t-\frac{3}{2} $$ power-law decay. For the vacuum block the transition occurs at t ≈ π c 6 h L $$ t\approx \frac{\uppi c}{6{h}_L} $$ , confirming analytic predictions. In the Euclidean regime, due to Stokes phenomena the naive semiclassical approximation fails completely in a finite region enclosing the ‘forbidden singularities’. We emphasize that limitations on the reconstruction of a local bulk should ultimately stem from distinctions between semiclassical and exact correlators.

Abstract Aspects of black hole thermodynamics and information loss can be derived as a consequence of Virasoro symmetry. To bolster the connection between Virasoro conformal blocks and AdS3 quantum gravity, we study sl(2) Chern-Simons Wilson line networks and revisit the idea that they compute a variety of CFT2 observables, including Virasoro OPE blocks, exactly. We verify this in the semiclassical large central charge limit and to low orders in a perturbative 1/c expansion. Wilson lines connecting the boundary to points in the bulk play a natural role in bulk reconstruction. Because quantum gravity in AdS3 is rigidly fixed by Virasoro symmetry, we argue that sl(2) Wilson lines provide building blocks for background independent bulk reconstruction. In particular, we show explicitly that they automatically ‘know’ about the uniformizing coordinates appropriate to any background state.

Abstract Recent work has demonstrated that black hole thermodynamics and information loss/restoration in AdS3/CFT2 can be derived almost entirely from the behavior of the Virasoro conformal blocks at large central charge, with relatively little dependence on the precise details of the CFT spectrum or OPE coefficients. Here, we elaborate on the non-perturbative behavior of Virasoro blocks by classifying all ‘saddles’ that can contribute for arbitrary values of external and internal operator dimensions in the semiclassical large central charge limit. The leading saddles, which determine the naive semiclassical behavior of the Virasoro blocks, all decay exponentially at late times, and at a rate that is independent of internal operator dimensions. Consequently, the semiclassical contribution of a finite number of high-energy states cannot resolve a well-known version of the information loss problem in AdS3. However, we identify two infinite classes of sub-leading saddles, and one of these classes does not decay at late times.

Abstract One can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in AdS3/CFT2. In this paper we use the technique to perform calculations in the small 1/c ∝ G N expansion: (1) we prove the all-orders resummation of logarithmic factors ∝ 1 c log z $$ \propto \frac{1}{c} \log\;z $$ in the Lorentzian regime, demonstrating that 1/c corrections directly shift Lyapunov exponents associated with chaos, as claimed in prior work, (2) we perform another all-orders resummation in the limit of large c with fixed cz, interpolating between the early onset of chaos and late time behavior, (3) we explicitly compute the Virasoro vacuum block to order 1/c 2 and 1/c 3 with external dimensions fixed, corresponding to 2 and 3 loop calculations in AdS3, and (4) we derive the heavy-light vacuum blocks in theories with N $$ \mathcal{N} $$ = 1, 2 superconformal symmetry.