arXiv subjects

Daniel L. Jafferis

Publications and source records attributed to Daniel L. Jafferis.

At least 19 recordsLinked to original sources

arXiv2026

Monitoring a de Sitter universe through an anti-de Sitter window

We propose that AdS$_3$ gravity coupled to dS$_2$ end-of-the-world branes is dual to a unitary holographic CFT$_2$ with non-unitary conformal boundary conditions. These boundary conditions have complex $g$-functions and appear in conjugate pairs. The associated gravitational path integral admits no real saddles, but does admit complex saddles. We show that an AdS$_3$ black hole microstate with a dS$_2$ brane behind the horizon corresponds to the unitary time evolution of a pure CFT state prepared by a Euclidean path integral on a cylinder with such boundary conditions. The construction predicts a boundary-condition-changing primary with $h=-c/8$, which resides in the boundary sector rather than the bulk spectrum and is therefore compatible with unitarity of the underlying CFT. This realizes dS holography as state preparation in a unitary AdS/CFT Hilbert space.

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arXiv2026

The many facets of a hyperbolic tetrahedron: open and closed triangulations of 3d gravity

We study a model of 3d gravity relevant to the open sector of a CFT ensemble. The quantum theory is the open Virasoro TQFT, obtained by restricting the full open-closed Virasoro TQFT to a subclass of admissible manifolds. We show that it computes gravitational path integrals on compact regions with fixed-length boundary conditions for states above the black hole threshold, and fixed-angle boundary conditions for states below the threshold. Focusing on a special class of manifolds involving only boundary Wilson loops, we further show that the relation between Conformal Turaev-Viro theory and the diagonal sector of two copies of Virasoro TQFT arises naturally from an open-closed duality.

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arXiv2025

On random matrix statistics of 3d gravity

We show that 3d gravity on manifolds that are topologically a Riemann surface times an interval $\Sigma_{g,n}\times I$ with end-of-the-world branes at the ends of the interval is described by a random matrix model, namely the Virasoro minimal string. Because these manifolds have $n$ annular asymptotic boundaries, the path integrals naturally correspond to spectral correlators of open strings upon inverse Laplace transforms. For $g=0$ and $n=2$, we carry out an explicit path integration and find precise agreement with the universal random matrix expression. For Riemann surfaces with negative Euler characteristic, we evaluate the path integral as a gravitational inner product between states prepared by two copies of Virasoro TQFT. Along the way, we clarify the effects of gauging the mapping class group and the connection to chiral 3d gravity.

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arXiv2025

Open-closed 3d gravity as a random ensemble

We investigate an ensemble of boundary CFTs within the framework of a tensor model recently constructed to model 3d quantum gravity. The incorporation of CFT borders introduces new elements to the gravity theory. In particular, it leads to an open-closed extension of Virasoro TQFT, which in the classical limit gives rise to 3d gravity with tensionful end-of-the-world branes. It also provides predictions for off-shell manifolds with bordered asymptotic boundaries, such as the annulus wormhole. As an application, we construct a purely open variant of the tensor model to study a purely open bootstrap problem in the context of CFT triangulation. We also briefly discuss the extension to non-orientable CFTs.

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arXiv2025

A disorder-averaged framework for evaluating the Witten index

We study supersymmetric indices in disordered systems, in particular an $\mathcal{N}=4$ supersymmetric Sachdev-Ye-Kitaev-type quantum mechanics. In cases where the disordered parameters do not affect the index, we explain how the exact answer can nevertheless be obtained using disorder averaged collective variables. Furthermore, when disorder averaging is performed on multiple copies of the same theory, non-trivial coupling between them is generated. We show how the index ultimately remains factorized.

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arXiv2024

3d Gravity as a random ensemble

We give further evidence that the matrix-tensor model studied in \cite{belin2023} is dual to AdS$_{3}$ gravity including the sum over topologies. This provides a 3D version of the duality between JT gravity and an ensemble of random Hamiltonians, in which the matrix and tensor provide random CFT$_2$ data subject to a potential that incorporates the bootstrap constraints. We show how the Feynman rules of the ensemble produce a sum over all three-manifolds and how surgery is implemented by the matrix integral. The partition functions of the resulting 3d gravity theory agree with Virasoro TQFT (VTQFT) on a fixed, hyperbolic manifold. However, on non-hyperbolic geometries, our 3d gravity theory differs from VTQFT, leading to a difference in the eigenvalue statistics of the associated ensemble. As explained in \cite{belin2023}, the Schwinger-Dyson (SD) equations of the matrix-tensor integral play a crucial role in understanding how gravity emerges in the limit that the ensemble localizes to exact CFT's. We show how the SD equations can be translated into a combinatorial problem about three-manifolds.

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arXiv2024

Thermal Bekenstein-Hawking entropy from the worldsheet

We define and compute the leading sphere diagram contribution to the entropy of the BTZ black hole supported by Kalb-Ramond flux in bosonic string theory. In a winding condensate description, integrating exactly over the constant mode for the radial direction of AdS$_3$ reduces the problem to one of the correlation functions of winding operators in the free theory. The volume of the residual PSL(2,$\mathbb{C}$) gauge group of the sphere is canceled by the action of conformal transformations on the winding interaction insertions. We formulate a precise version of the replica trick in terms of (infinitesimally) non-integer winding condensates to produce the entropy of the BTZ black hole. The resulting entropy can be calculated from the one-point function of a non-local operator on the worldsheet.

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arXiv2024

Double winding condensate CFT

We conjecture a two-dimensional conformal field theory built out of a linear dilaton and a compact $βγ$ system deformed by winding condensates on each of the compact cycles. In particular, explicit expressions of the residues of the correlation functions are provided. As a worldsheet theory, it describes a stringy black hole in AdS$_3$ (supported by the Kalb-Ramond flux) at the Hawking-Page temperature. It is expected to be connected to the Horowitz-Polchinski-like solution near the Hagedorn temperature of thermal AdS$_3$ and Euclidean BTZ blackhole as we vary the temperature.

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arXiv2024

The 2d Free Boson Minkowski CFT with Asymptotic Charges

We explicitly construct the states of the 2d free boson on the infinite line with specified asymptotic charges. The Minkowski CFT states derive from (the analytic continuation of) the shrinking limit of Euclidean angular quantization, wherein the superselection sector for fixed asymptotic charges corresponds to specific endpoint operators for the angular quantization on the sphere. When applied to string theory, we obtain a new class of fundamental strings that are neither open nor closed and which we dub "stretched strings". We describe constant-time snapshots of the worldsheets of the different types of stretched strings, and as a special case we find a heuristic picture of Maldacena's "long strings" in the $c=1$ string theory.

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arXiv2024

Stretched horizon, replica trick and off-shell winding condensate, and all that

$\alpha'$ corrections to near-horizon dynamics of a Schwarzschild black hole in a large number of spacetime dimensions $D$ are governed by the worldsheet theory composed of the cigar CFT and the classical sigma model on the sphere at the horizon, along with a timelike-Liouville theory of central charge $26-D$. At leading order in weak string coupling, blackhole thermodynamics is insensitive to the details of timelike Liouville theory. In this limit, we use Lewkowycz-Maldacena-trick motivated infinitesimally off-shell closed string worldsheet formalism in [arxiv: 2310.02313] to calculate thermal entropy exactly in $\alpha'$. The leading term in $\alpha'\to 0$ limit and the first stringy correction of our result are in precise agreement with the target space Callan-Myers-Perry formula.

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arXiv2023

AdS$_3$ String Stars at Pure NSNS Flux

We study Horowitz-Polchinski string stars in pure AdS$_3$ near the Hagedorn temperature using the technique of worldsheet conformal perturbation theory. Since the worldsheet CFT for pure AdS$_3$ is known exactly, our methodology provides a systematic way to construct Horowitz-Polchinski backgrounds to all orders in $α'$. We explicitly construct the leading string star equations in a double expansion in temperature and WZW level $k$ which we then solve numerically.

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arXiv2022

Stringy ER=EPR

The ER = EPR correspondence relates a superposition of entangled, disconnected spacetimes to a connected spacetime with an Einstein-Rosen bridge. We construct examples in which both sides may be described by weakly-coupled string theory. The relation between them is given by a Lorentzian continuation of the FZZ duality of the two-dimensional Euclidean black hole CFT in one example, and in another example by continuation of a similar duality that we propose for the asymptotic Euclidean AdS3 black hole. This gives a microscopic understanding of ER = EPR: one has a worldsheet duality between string theory in a connected, eternal black hole, and in a superposition of disconnected geometries in an entangled state. The disconnected description includes a condensate of entangled folded strings emanating from a strong-coupling region in place of a horizon. Our construction relies on a Lorentzian interpretation of Euclidean time winding operators via angular quantization, as well as some lesser known worldsheet string theories, such as perturbation theory around a thermofield-double state, which we define using Schwinger-Keldysh contours in target space.

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arXiv2022

Angular Quantization in CFT

The most common quantization scheme in which to study a conformal field theory is radial quantization, wherein a Hilbert space of states is defined on a sphere, whose Hamiltonian when mapped to the plane is the dilatation generator and which boasts a state/operator correspondence. In this paper, we consider an alternative quantization scheme for 2d CFTs in which the plane is foliated by constant-angle slices, as opposed to concentric circles, whose Hamiltonian is the rotation generator. In this angular quantization, there is no state/operator correspondence but instead an "asymptotics/operator correspondence". A central feature is that the quantization slice ends on two operators, and a regulator must be chosen by excising holes around each operator and imposing suitable boundary conditions such that the holes shrink to the desired local operators. This angular quantization may be viewed as constructing CFTs in Minkowski space, or separately as studying non-conformal (but local) boundary conditions in CFTs. We provide explicit Fock space constructions for various free 2d CFTs. In addition to the motivation of applying angular quantization in string theory situations where traditional radial quantization is insufficient, we comment on its relation to modular Hamiltonian approaches to entanglement entropy.

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arXiv2017

On the construction of charged operators inside an eternal black hole

We revisit the holographic construction of (approximately) local bulk operators inside an eternal AdS black hole in terms of operators in the boundary CFTs. If the bulk operator carries charge, the construction must involve a qualitatively new object: a Wilson line that stretches between the two boundaries of the eternal black hole. This operator - more precisely, its zero mode - cannot be expressed in terms of the boundary currents and only exists in entangled states dual to two-sided geometries, which suggests that it is a state-dependent operator. We determine the action of the Wilson line on the relevant subspaces of the total Hilbert space, and show that it behaves as a local operator from the point of view of either CFT. For the case of three bulk dimensions, we give explicit expressions for the charged bulk field and the Wilson line. Furthermore, we show that when acting on the thermofield double state, the Wilson line may be extracted from a limit of certain standard CFT operator expressions. We also comment on the relationship between the Wilson line and previously discussed mirror operators in the eternal black hole.

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arXiv2016

Toda Theory From Six Dimensions

We describe a compactification of the six-dimensional (2,0) theory on a four-sphere which gives rise to a two-dimensional Toda theory at long distances. This construction realizes chiral Toda fields as edge modes trapped near the poles of the sphere. We relate our setup to compactifications of the (2,0) theory on the five and six-sphere. In this way, we explain a connection between half-BPS operators of the (2,0) theory and two-dimensional W-algebras, and derive an equality between their conformal anomalies. As we explain, all such relationships between the six-dimensional (2,0) theory and Toda field theory can be interpreted as statements about the edge modes of complex Chern-Simons on various three-manifolds with boundary.

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arXiv2015

Relative entropy equals bulk relative entropy

We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

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arXiv2015

The string origin of dyonic ${\cal N}=8$ supergravity and its simple Chern-Simons duals

We clarify the higher-dimensional origin of a class of dyonic gaugings of $D=4$ ${\cal N}=8$ supergravity recently discovered, when the gauge group is chosen to be ISO(7). This dyonically-gauged maximal supergravity arises from consistent truncation of massive IIA supergravity on $S^6$, and its magnetic coupling constant descends directly from the Romans mass. The critical points of the supergravity uplift to new AdS$_4$ massive type IIA vacua. We identify the corresponding CFT$_3$ duals as super-Chern-Simons-matter theories with simple gauge group SU$(N)$, with level $k$ given by the Romans mass. In particular, we find a critical point that uplifts to the first explicit ${\cal N}=2$ AdS$_4$ massive IIA background. We compute its free energy and that of the candidate dual Chern-Simons theory by localisation to a solvable matrix model, and find perfect agreement. This provides the first AdS$_4$/CFT$_3$ precision match in massive type IIA string theory.

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arXiv2015

Quasinormal Quantization in deSitter Spacetime

A scalar field in four-dimensional deSitter spacetime (dS_4) has quasinormal modes which are singular on the past horizon of the south pole and decay exponentially towards the future. These are found to lie in two complex highest-weight representations of the dS_4 isometry group SO(4,1). The Klein-Gordon norm cannot be used for quantization of these modes because it diverges. However a modified `R-norm', which involves reflection across the equator of a spatial S^3 slice, is nonsingular. The quasinormal modes are shown to provide a complete orthogonal basis with respect to the R-norm. Adopting the associated R-adjoint effectively transforms SO(4,1) to the symmetry group SO(3,2) of a 2+1-dimensional CFT. It is further shown that the conventional Euclidean vacuum may be defined as the state annihilated by half of the quasinormal modes, and the Euclidean Green function obtained from a simple mode sum. Quasinormal quantization contrasts with some conventional approaches in that it maintains manifest dS-invariance throughout. The results are expected to generalize to other dimensions and spins.

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