Quantum extremal surfaces are central to the connection between quantum information theory and quantum gravity and they have played a prominent role in the recent progress on the information paradox. We initiate a program to systematically link these
surfaces to the microscopic data of the dual conformal field theory, namely the scaling dimensions of local operators and their OPE coefficients. We consider CFT states obtained by acting on the vacuum with single-trace operators, which are dual to one-particle states of the bulk theory. Focusing on AdS$_3$/CFT$_2$, we compute the CFT entanglement entropy to second order in the large $c$ expansion where quantum extremality becomes important and match it to the expectation value of the bulk area operator. We show that to this order, the Virasoro identity block contributes solely to the area operator.
We generalize the eigenstate thermalization hypothesis to systems with global symmetries. We present t
We study correlation functions involving generalized ANEC operators of the form $int dx^- left(x^-right)^{n+2} T_{--}(vec{x})$ in four dimensions. We compute two, three, and four-point functions involving external scalar states in both free and holog
raphic Conformal Field Theories. From this information, we extract the algebra of these light-ray operators. We find a global subalgebra spanned by $n={-2, -1, 0, 1, 2}$ which annihilate the conformally invariant vacuum and transform among themselves under the action of the collinear conformal group that preserves the light-ray. Operators outside this range give rise to an infinite central term, in agreement with previous suggestions in the literature. In free theories, even some of the operators inside the global subalgebra fail to commute when placed at spacelike separation on the same null-plane. This lack of commutativity is not integrable, presenting an obstruction to the construction of a well defined light-ray algebra at coincident $vec{x}$ coordinates. For holographic CFTs the behavior worsens and operators with $n eq -2$ fail to commute at spacelike separation. We reproduce this result in the bulk of AdS where we present new exact shockwave solutions dual to the insertions of these (exponentiated) operators on the boundary.
A common method to prepare states in AdS/CFT is to perform the Euclidean path integral with sources turned on for single-trace operators. These states can be interpreted as coherent states of the bulk quantum theory associated to Lorentzian initial d
ata on a Cauchy slice. In this paper, we discuss the extent to which arbitrary initial data can be obtained in this way. We show that the initial data must be analytic and define the subset of it that can be prepared by imposing bulk regularity. Turning this around, we show that for generic analytic initial data the corresponding Euclidean section contains singularities coming from delta function sources in the bulk. We propose an interpretation of these singularities as non-perturbative objects in the microscopic theory.
We propose an ansatz for OPE coefficients in chaotic conformal field theories which generalizes the Eigenstate Thermalization Hypothesis and describes any OPE coefficient involving heavy operators as a random variable with a Gaussian distribution. In
two dimensions this ansatz enables us to compute higher moments of the OPE coefficients and analyse two and four-point functions of OPE coefficients, which we relate to genus-2 partition functions and their squares. We compare the results of our ansatz to solutions of Einstein gravity in AdS$_3$, including a Euclidean wormhole that connects two genus-2 surfaces. Our ansatz reproduces the non-perturbative correction of the wormhole, giving it a physical interpretation in terms of OPE statistics. We propose that calculations performed within the semi-classical low-energy gravitational theory are only sensitive to the random nature of OPE coefficients, which explains the apparent lack of factorization in products of partition functions.
We study a $T^2$ deformation of large $N$ conformal field theories, a higher dimensional generalization of the $Tbar T$ deformation. The deformed partition function satisfies a flow equation of the diffusion type. We solve this equation by finding it
s diffusion kernel, which is given by the Euclidean gravitational path integral in $d+1$ dimensions between two boundaries with Dirichlet boundary conditions for the metric. This is natural given the connection between the flow equation and the Wheeler-DeWitt equation, on which we offer a new perspective by giving a gauge-invariant relation between the deformed partition function and the radial WDW wave function. An interesting output of the flow equation is the gravitational path integral measure which is consistent with a constrained phase space quantization. Finally, we comment on the relation between the radial wave function and the Hartle-Hawking wave functions dual to states in the CFT, and propose a way of obtaining the volume of the maximal slice from the $T^2$ deformation.
We explore large-$N$ symmetric orbifolds of the $mathcal N=2$ minimal models, and find evidence that their moduli spaces each contain a supergravity point. We identify single-trace exactly marginal operators that deform them away from the symmetric o
rbifold locus. We also show that their elliptic genera exhibit slow growth consistent with supergravity spectra in AdS$_3$. We thus propose an infinite family of new holographic CFTs.
We study quantum corrections to holographic entanglement entropy in AdS$_3$/CFT$_2$; these are given by the bulk entanglement entropy across the Ryu-Takayanagi surface for all fields in the effective gravitational theory. We consider bulk $U(1)$ gaug
e fields and gravitons, whose dynamics in AdS$_3$ are governed by Chern-Simons terms and are therefore topological. In this case the relevant Hilbert space is that of the edge excitations. A novelty of the holographic construction is that such modes live not only on the bulk entanglement cut but also on the AdS boundary. We describe the interplay of these excitations and provide an explicit map to the appropriate extended Hilbert space. We compute the bulk entanglement entropy for the CFT vacuum state and find that the effect of the bulk entanglement entropy is to renormalize the relation between the effective holographic central charge and Newtons constant. We also consider excited states obtained by acting with the $U(1)$ current on the vacuum, and compute the difference in bulk entanglement entropy between these states and the vacuum. We compute this UV-finite difference both in the bulk and in the CFT finding a perfect agreement.
We investigate the growth of Fourier coefficients of Siegel paramodular forms built by exponentially lifting weak Jacobi forms, focusing on terms with large negative discriminant. To this end we implement a method based on deforming contours that exp
resses the coefficients of all such terms as residues. We find that there are two types of weak Jacobi forms, leading to two different growth behaviors: the more common type leads to fast, exponential growth, whereas a second type leads to slower growth, akin to the growth seen in ratios of theta functions. We give a simple criterion to distinguish between the two types, and give a simple closed form expression for the coefficients in the slow growing case. In a companion article [1], we provide physical applications of these results to symmetric product orbifolds and holography.
We investigate the growth of coefficients in the elliptic genus of symmetric product orbifolds at large central charge. We find that this landscape decomposes into two regions. In one region, the growth of the low energy states is Hagedorn, which ind
icates a stringy dual. In the other, the growth is much slower, and compatible with the spectrum of a supergravity theory on AdS$_3$. We provide a simple diagnostic which places any symmetric product orbifold in either region. We construct a class of elliptic genera with such supergravity-like growth, indicating the possible existence of new realizations of AdS$_3$/CFT$_2$ where the bulk is a semi-classical supergravity theory. In such cases, we give exact expressions for the BPS degeneracies, which could be matched with the spectrum of perturbative states in a dual supergravity description.
