42 research outputs found

    On CFT and Quantum Chaos

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    We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.Comment: 26 pages, 2 figures. References adde

    Defects in Jackiw-Teitelboim Quantum Gravity

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    We classify and study defects in 2d Jackiw-Teitelboim gravity. We show these are holographically described by a deformation of the Schwarzian theory where the reparametrization mode is integrated over different coadjoint orbits of the Virasoro group. We show that the quantization of each coadjoint orbit is connected to 2d Liouville CFT between branes with insertions of Verlinde loop operators. We also propose an interpretation for the exceptional orbits. We use this perspective to solve these deformations of the Schwarzian theory, computing their partition function and correlators. In the process, we define two geometric observables: the horizon area operator Φh\Phi_h and the geodesic length operator L(γ)L(\gamma). We show this procedure is structurally related to the deformation of the particle-on-a-group quantum mechanics by the addition of a chemical potential. As an example, we solve the low-energy theory of complex SYK with a U(1) symmetry and generalize to the non-abelian case.Comment: 66 pages, v4: clarifications added, typos corrected, matches published versio

    Decoherence and Loss of Entanglement in Acoustic Black Holes

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    We studied the process of decoherence in acoustic black holes. We focused on the ion trap model proposed by Horstmann et al. (Phys. Rev. Lett. 104, 250403 (2010)) but the formalism is general to any experimental implementation. For that particular setup, we computed the decoherence time for the experimental parameters that they proposed. We found that a quantum to classical transition occurs during the measurement and we proposed improved parameters to avoid such a feature. We also studied the entanglement between the Hawking-pair phonons for an acoustic black hole while in contact with a reservoir, through the quantum correlations, showing that they remain strongly correlated for small enough times and temperatures.Comment: 5 pages, 2 figures, accepted in Phys. Rev. Let


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    We relate Liouville/Toda CFT correlators on Riemann surfaces with boundaries and cross-cap states to supersymmetric observables in four-dimensional N=2 gauge theories. Our construction naturally involves four-dimensional theories with fields defined on different Z2_2 quotients of the sphere (hemisphere and projective space) but nevertheless interacting with each other. The six-dimensional origin is a Z2_2 quotient of the setup giving rise to the usual AGT correspondence. To test the correspondence, we work out the RP4^4 partition function of four-dimensional N=2 theories by combining a 3d lens space and a 4d hemisphere partition functions. The same technique reproduces known RP2^2 partition functions in a form that lets us easily check two-dimensional Seiberg-like dualities on this nonorientable space. As a bonus we work out boundary and cross-cap wavefunctions in Toda CFT.Comment: 56 pages. v2: Clarify discrete theta angle. v3: Published in JHEP; extra references. v4: Minor sign fix; extra reference

    New insights on near-extremal black holes

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    We describe two puzzles that arise from a semiclassical treatment of near-extremal black hole thermodynamics. Both puzzles are resolved by realizing that quantum corrections become arbitrarily large at low temperatures, and we explain how the spectrum and dynamics of near-extremal black holes are modified. This analysis also implies that without low energy supersymmetry, such as in the real world, extremal black holes at exactly zero temperature do not exist since the classical picture breaks down completely. In the context of supergravity the analysis is modified; supersymmetric extremal black holes do exist and they are separated from the non-extremal spectrum by a gap power-law suppressed in the entropy. This justifies black hole microstate counting performed in the 90's using string theory.Comment: 13 pp; Short article written for the ICTS Newslette

    Bounds on OPE Coefficients from Interference Effects in the Conformal Collider

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    We apply the average null energy condition to obtain upper bounds on the three-point function coefficients of stress tensors and a scalar operator, TTO,\langle TT {\cal O } \rangle, in general CFTs. We also constrain the gravitational anomaly of U(1)U(1) currents in four-dimensional CFTs, which are encoded in three-point functions of the form TTJ\langle TT J \rangle. In theories with a large NN AdS dual we translate these bounds into constraints on the coefficient of a higher derivative bulk term of the form ϕW2\int \phi\hspace{.5mm} W^2 . We speculate that these bounds also apply in de-Sitter. In this case our results constrain inflationary observables, such as the amplitude for chiral gravity waves that originate from higher derivative terms in the Lagrangian of the form ϕWW\phi \hspace{.5mm}W W^*.Comment: 46 pages, 3 figure

    Spin-Statistics for Black Hole Microstates

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    The gravitational path integral can be used to compute the number of black hole states for a given energy window, or the free energy in a thermal ensemble. In this article we explain how to use the gravitational path integral to compute the separate number of bosonic and fermionic black hole microstates. We do this by comparing the partition function with and without the insertion of (1)F(-1)^{\sf F}. In particular we introduce a universal rotating black hole that contributes to the partition function in the presence of (1)F(-1)^{\sf F}. We study this problem for black holes in asymptotically flat space and in AdS, putting constraints on the high energy spectrum of holographic CFTs (not necessarily supersymmetric). Finally, we analyze wormhole contributions to related quantities.Comment: 34 pages; v2: references adde