arXiv subjects

Jeevan Chandra

Publications and source records attributed to Jeevan Chandra.

11 recordsLinked to original sources

arXiv2026

Positivity constraints on the dynamics of cusped impurities in CFTs

The cusp anomalous dimension is the universal logarithmic contribution to the free energy of a line defect with a cusp, and provides a useful observable characterizing defect dynamics. We generalize this notion to cusped line defects in the presence of a planar conformal boundary or interface. The geometry is characterized by three angles, and the distance of the cusp from the boundary or interface which separates short-distance and long-distance regimes. The resulting free energy contains two large logarithmic terms: a short-distance contribution governed by the usual vacuum cusp anomalous dimension, and a new long-distance contribution sensitive to the boundary or interface. Using reflection positivity for transverse deformations of the defect rays, we derive several constraints on the coefficients of these logarithmic terms, which can be packaged into negative semi-definiteness of their angular Hessians. We also derive constraints on the continuation of these coefficients to Lorentzian kinematics. We compute these coefficients and verify the constraints explicitly in free scalar and Maxwell theories and in planar $\mathcal N=4$ super-Yang-Mills theory at weak coupling for various choices of boundary conditions. At strong coupling, we compute the logarithmic coefficients in the holographic D3-D5 defect CFT and find a Gross-Ooguri-like phase transition between competing string worldsheets driven by the geometry of the cusp relative to the interface. We also observe a close connection of the cusp free energy in this setup with holographic corner entanglement entropy.

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arXiv2026

Elastic stiffness of three-dimensional black holes and wormholes from Liouville line defects

We study elastic deformations of thin-shell black holes and wormholes in AdS$_3$ gravity. These geometries are sourced by line defects in the dual conformal field theory, and their shape and mass distribution define elastic moduli of the gravitational saddle. We compute the quadratic response of the partition function to these deformations, defining stiffness kernels for both transverse shape fluctuations and inhomogeneous mass-density fluctuations. The computation of the stiffness kernels can be realized as a hyperbolic response to a conformal welding problem which reduces to the universal Schwarzian response in the heavy-shell limit. The stiffness kernels are two-point functions of defect-local operators in CFT: the displacement operator, which measures the response to shape deformations, and a mass-density operator, which measures the response to local changes in the shell density. We compute the spectrum of these operators in the semiclassical limit, in various black hole and wormhole backgrounds. The spectrum can be discrete or continuous depending on the existence of a non-compact direction transverse to the shell in the geometry. We also provide a Lorentzian interpretation for the stiffness kernels using linear response theory and compute the relaxation time scales towards the corresponding transient deformations in the dual holographic CFT. Lastly, we compute the effect of these elastic deformations on black hole microstate statistics and black hole entropy.

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arXiv2026

Line Defects in Liouville Conformal Field Theory: Localized Cosmological Constants and Decohered Hyperbolic Geometries

The study of quantum impurities has long been a central and inspiring theme in quantum many-body physics. Localized impurities are modeled by line defects in quantum field theory. We describe a line defect in Liouville CFT realized as a ``localized cosmological constant'': a non-topological line insertion into the Liouville path integral that is tractable at both weak and strong defect coupling. At weak coupling, we analyze the defect perturbatively and characterize it through its correlations with local operators, energy and information transport, the Casimir energies associated with fusion, and corrections to the open string channel spectrum. We also study the effect of a cuspidal deformation of the defect locus on these observables and describe novel monotonicity properties as the cusp angle is varied. These results derived using perturbation theory are more generally applicable to pinning defects constructed from scalar primary operators in compact $2d$ CFTs. At strong coupling, in a semiclassical limit, the defect admits a geometric interpretation in terms of a discontinuity in the extrinsic curvature of the $1d$ defect locus embedded in $2d$ hyperbolic geometries. The observables characterizing the defect in this regime are computed by gluing hyperbolic surfaces across the defect, and are compared with the corresponding weak coupling results. The correlations across the defect, both at weak and strong coupling, can also be realized by an effective ``decohered FZZT interface'' constructed by diagonal gluing of two copies of the fixed-length FZZT boundary state. These line defects also have interesting interpretations in other models, in terms of end-of-the-world branes in Jackiw-Teitelboim gravity, dust shells in AdS$_3$ gravity, and interfaces with a proliferation of non-abelian Wilson loops in $4d$ $\mathcal{N}=2$ gauge theories.

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arXiv2025

Statistics in 3d gravity from knots and links

In recent years, there has been remarkable progress in evaluating wormhole amplitudes in 3d Einstein gravity with negative cosmological constant and matching them to statistics of 2d CFT data. In this work, we compute non-perturbative Gaussian and non-Gaussian gravitational contributions to the OPE statistics using a framework that can systematically generate a class of such non-perturbative effects - \textit{Fragmentation of knots and links by Wilson lines}. We illustrate this idea by constructing multi-boundary wormholes from fragmentation diagrams of prime knots and links with upto five crossings. We discuss fragmentations of hyperbolic knots and links like the figure-eight knot, the three-twist knot and the Whitehead link; and non-hyperbolic ones like the Hopf link, the trefoil knot, the Solomon's knot and the Cinquefoil knot. Using Virasoro TQFT, we show how the partition functions on wormholes constructed from different fragmentations of the same knot or link are closely related. Using these fragmentations, we compute gravitational contributions to the variance, a two-point non-Gaussianity, two structures of four-point non-Gaussianities called the `pillow contraction' and the `$6j$-contraction', and some six-point non-Gaussianities. We also check the consistency of some of these non-Gaussianities with the extended Gaussian ensemble of OPE data that incorporates the Gaussian corrections to the variance from knots.

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arXiv2025

Rademacher expansion of modular integrals

We develop a method to evaluate integrals of non-holomorphic modular functions over the fundamental domain of the torus with modular parameter $\tau$ analytically. It proceeds in two steps: first the integral is transformed to a Lorentzian contour by the same strategy that leads to the Lorentzian inversion formula in CFT, and then we apply a two-dimensional version of the Rademacher expansion. This computes the integral in terms of an expansion sensitive to the singular behaviour of the integrand near all the Lorentzian cusps $\tau \to i \infty$, $\bar{\tau} \to x \in \mathbb{Q}$. We apply this technique to a variety of examples such as the evaluation of string one-loop partition functions, where it leads to the first analytic formula for the cosmological constants of the bosonic string and the $\mathrm{SO}(16) \times \mathrm{SO}(16)$ string.

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arXiv2024

Euclidean wormholes in holographic RG flows

We describe a one-parameter family of Euclidean wormhole solutions with the topology of a compact hyperbolic space times an interval in Einstein gravity minimally coupled to a massless scalar field in AdS$_{d+1}$ commonly referred to as Einstein-dilaton gravity. These solutions are locally described by the same metric and dilaton profile as the single-boundary Janus domain wall solutions in the same theory which are usually studied in the context of holographic RG flows. The wormholes compute the averaged product of partition functions of CFTs on either boundary deformed by different marginal couplings to the scalar operator dual to the dilaton. We observe that the renormalised volumes of these wormholes increase monotonically with the difference in the marginal couplings on the boundary thereby showing that the pair of CFTs on the boundaries get increasingly decorrelated as the difference in the marginal couplings increases. We use the partition functions of the three-dimensional wormhole solutions to determine the variance of the OPE data of local operators between the marginally deformed 2d CFTs and quantify how the variance decays with the difference in marginal couplings. In addition, a family of wormholes sourced by a thin shell of dust determine how the variance of the matrix elements of the dual line defect decays with the difference in marginal couplings. Applying the GKPW dictionary to wormholes, we compute averages of integrated dilaton correlators treating the wormhole amplitude as a functional of the dilaton sources. We observe that the crossed two-point correlators with a dilaton insertion on either boundary decay montonically with the difference in marginal couplings consistent with the observation that the CFTs increasingly decorrelate as the difference in marginal couplings grows.

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arXiv2024

Statistics of three-dimensional black holes from Liouville line defects

Black holes and wormholes in the gravitational path integral can be used to calculate the statistics of heavy operators. An explicit example in higher dimensions is provided by thin shells of matter. We study these solutions in 3D gravity, and reproduce the behavior of black holes and wormholes from the dual CFT using the large-$c$ conformal bootstrap. The CFT operator that creates a thin shell black hole is a line defect, so we begin by using the bootstrap to study the statistics of line defects, both at finite $c$ and in the holographic large-$c$ limit. The crossing equation leads to a universal formula for the average high-energy matrix elements of the line defect in any compact, unitary 2d CFT with $c>1$. The asymptotics are controlled by a line defect in Liouville CFT at the same value of the central charge. At large $c$, three distinct quantities are related: The statistics of line defects in holographic CFTs, the individual matrix elements of a line defect in Liouville CFT, and the on-shell action of black holes and wormholes in 3D gravity. The three calculations match for black holes, and if the statistics of the line defects are assumed to be approximately Gaussian, then a class of wormholes is also reproduced by the dual CFT.

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arXiv2023

Euclidean wormholes for individual 2d CFTs

We interpret appropriate families of Euclidean wormhole solutions of AdS$_3$ gravity in individual 2d CFTs as replica wormholes described by branching around the time-symmetric apparent horizons of black holes sourced by the backreaction of heavy point particles. These wormholes help describe a rich formalism to coarse grain pure states in 2d CFTs dual to the black hole geometries because the wormhole amplitudes match with the Renyi entropies of CFT states obtained by decohering the pure states in a specific way. This formalism can be generalised to coarse grain pure states in several copies of the dual CFT dual to multi-boundary black holes using wormhole solutions with higher genus boundaries using which we illustrate that coarse graining away the interior of multi-boundary black holes sets the mutual information between any two copies of the dual CFT to zero. Furthermore, this formalism of coarse graining pure states can be extended to decohere transition matrices between pure states which helps interpret more general families of wormhole solutions including those with non replica-symmetric boundary conditions in individual CFTs. The pseudo entropy of the decohered transition matrices has interesting holographic interpretation in terms of the area of minimal surfaces on appropriate black hole or wormhole geometries. The wormhole solutions which show up in the coarse graining formalism also compute the Renyi entropies of Hawking radiation after the Page time in a setup which generalizes the West Coast model to 3d gravity. Using this setup, we discuss the evaporation of one-sided black holes sourced by massive point particles and multi-boundary black holes in 3d gravity.

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arXiv2023

Toward random tensor networks and holographic codes in CFT

In holographic CFTs satisfying eigenstate thermalization, there is a regime where the operator product expansion can be approximated by a random tensor network. The geometry of the tensor network corresponds to a spatial slice in the holographic dual, with the tensors discretizing the radial direction. In spherically symmetric states in any dimension and more general states in 2d CFT, this leads to a holographic error-correcting code, defined in terms of OPE data, that can be systematically corrected beyond the random tensor approximation. The code is shown to be isometric for light operators outside the horizon, and non-isometric inside, as expected from general arguments about bulk reconstruction. The transition at the horizon occurs due to a subtle breakdown of the Virasoro identity block approximation in states with a complex interior.

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arXiv2022

Coarse graining pure states in AdS/CFT

We construct new Euclidean wormhole solutions in AdS(d+1) and discuss their role in UV-complete theories, without ensemble averaging. The geometries are interpreted as overlaps of GHZ-like entangled states, which arise naturally from coarse graining the density matrix of a pure state in the dual CFT. In several examples, including thin-shell collapsing black holes and pure black holes with an end-of-the-world brane behind the horizon, the coarse-graining map is found explicitly in CFT terms, and used to define a coarse-grained entropy that is equal to one quarter the area of a time-symmetric apparent horizon. Wormholes are used to derive the coarse-graining map and to study statistical properties of the quantum state. This reproduces aspects of the West Coast model of 2D gravity and the large-c ensemble of 3D gravity, including a Page curve, in a higher-dimensional context with generic matter fields.

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arXiv2022

Semiclassical 3D gravity as an average of large-c CFTs

A two-dimensional CFT dual to a semiclassical theory of gravity in three dimensions must have a large central charge $c$ and a sparse low energy spectrum. This constrains the OPE coefficients and density of states of the CFT via the conformal bootstrap. We define an ensemble of CFT data by averaging over OPE coefficients subject to these bootstrap constraints, and show that calculations in this ensemble reproduce semiclassical 3D gravity. We analyze a wide variety of gravitational solutions, both in pure Einstein gravity and gravity coupled to massive point particles, including Euclidean wormholes with multiple boundaries and higher topology spacetimes with a single boundary. In all cases we find that the on-shell action of gravity agrees with the ensemble-averaged CFT at large $c$. The one-loop corrections also match in the cases where they have been computed. We also show that the bulk effective theory has random couplings induced by wormholes, providing a controlled, semiclassical realization of the mechanism of Coleman, Giddings, and Strominger.

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