11,388 research outputs found

    Genus Two Partition Functions and Renyi Entropies of Large c CFTs

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    We compute genus two partition functions in two dimensional conformal field theories at large central charge, focusing on surfaces that give the third Renyi entropy of two intervals. We compute this for generalized free theories and for symmetric orbifolds, and compare it to the result in pure gravity. We find a new phase transition if the theory contains a light operator of dimension Δ0.19\Delta\leq0.19. This means in particular that unlike the second Renyi entropy, the third one is no longer universal.Comment: 28 pages + Appendice

    Orbital Circularization of a Planet Accreting Disk Gas: Formation of Distant Jupiters in Circular Orbits based on Core Accretion Model

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    Recently, gas giant planets in nearly circular orbits with large semimajor axes (aa \sim 30--1000AU) have been detected by direct imaging. We have investigated orbital evolution in a formation scenario for such planets, based on core accretion model: i) Icy cores accrete from planetesimals at \lesssim 30AU, ii) they are scattered outward by an emerging nearby gas giant to acquire highly eccentric orbits, and iii) their orbits are circularized through accretion of disk gas in outer regions, where they spend most of time. We analytically derived equations to describe the orbital circularization through the gas accretion. Numerical integrations of these equations show that the eccentricity decreases by a factor of more than 5 during the planetary mass increases by a factor of 10. Because runaway gas accretion increases planetary mass by \sim 10--300, the orbits are sufficiently circularized. On the other hand, aa is reduced at most only by a factor of 2, leaving the planets in outer regions. If the relative velocity damping by shock is considered, the circularization is slowed down, but still efficient enough. Therefore, this scenario potentially accounts for the formation of observed distant jupiters in nearly circular orbits. If the apocenter distances of the scattered cores are larger than the disk sizes, their aa shrink to a quarter of the disk sizes; the aa-distribution of distant giants could reflect outer edges of the disks in a similar way that those of hot jupiters may reflect inner edges.Comment: 28 pages, 13 figures, accepted for publication in Ap

    Twist-nontwist correlators in M^N/S_N orbifold CFTs

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    We consider general 2D orbifold CFTs of the form M^N/S_N, with M a target space manifold and S_N the symmetric group, and generalize the Lunin-Mathur covering space technique in two ways. First, we consider excitations of twist operators by modes of fields that are not twisted by that operator, and show how to account for these excitations when computing correlation functions in the covering space. Second, we consider non-twist sector operators and show how to include the effects of these insertions in the covering space. We work two examples, one using a simple bosonic CFT, and one using the D1-D5 CFT at the orbifold point. We show that the resulting correlators have the correct form for a 2D CFT.Comment: 30 pages, 1 figure, additional reference adde

    Operator mixing for string states in the D1-D5 CFT near the orbifold point

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    In the context of the fuzzball programme, we investigate deforming the microscopic string description of the D1-D5 system on T^4xS^1 away from the orbifold point. Using conformal perturbation theory and a generalization of Lunin-Mathur symmetric orbifold technology for computing twist-nontwist correlators developed in a companion work, we initiate a program to compute the anomalous dimensions of low-lying string states in the D1-D5 superconformal field theory. Our method entails finding four-point functions involving a string operator O of interest and the deformation operator, taking coincidence limits to identify which other operators mix with O, subtracting the identified conformal family to isolate other contributions to the four-point function, finding the mixing coefficients, and iterating. For the lowest-lying string modes, this procedure should truncate in a finite number of steps. We check our method by showing how the operator dual to the dilaton does not participate in mixing that would change its conformal dimension, as expected. Next we complete the first stage of the iteration procedure for a low-lying string state of the form \partial X \partial X \bar\partial X \bar\partial X and find its mixing coefficient. Our main qualitative result is evidence of operator mixing at first order in the deformation parameter, which means that the string state acquires an anomalous dimension. After diagonalization this will mean that anomalous dimensions of some string states in the D1-D5 SCFT must decrease away from the orbifold point while others increase.Comment: 43 pages, added references and a commen

    Bosonization, cocycles, and the D1-D5 CFT on the covering surface

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    We consider the D1-D5 CFT near the orbifold point, specifically the computation of correlators involving twist sector fields using covering surface techniques. As is well known, certain twists introduce spin fields on the cover. Here we consider the bosonization of fermions to facilitate computations involving the spin fields. We find a set of cocycle operators that satisfy constraints coming from various SU(2)SU(2) symmetries, including the SU(2)L×SU(2)RSU(2)_L\times SU(2)_R R-symmetry. Using these cocycles, we consider the correlator of four spin fields on the cover, and show that it is invariant under all of the SU(2)SU(2) symmetries of the theory. We consider the mutual locality of operators, and compute several three-point functions. These computations lead us to a notion of radial ordering on the cover that is inherited from the original computation before lifting. Further, we note that summing over orbifold images sets certain branch-cut ambiguous correlators to zero.Comment: 29 pages, 1 figur

    3D MHD Simulations of Planet Migration in Turbulent Stratified Disks

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    We performed 3D MHD simulations of planet migration in stratified disks using the Godunov code PLUTO, where the disk is turbulent due to the magnetorotational instability. We study the migration for planets with different planet-star mass ratios q=Mp/Msq=M_{p}/M_{s}. In agreement with previous studies, for the low-mass planet cases (q=5×106q=5\times10^{-6} and 10510^{-5}), migration is dominated by random fluctuations in the torque. For a Jupiter-mass planet (q=Mp/Ms=103(q=M_{p}/M_{s}=10^{-3} for Ms=1M)M_{s}=1M_{\odot}), we find a reduction of the magnetic stress inside the orbit of the planet and around the gap region. After an initial stage where the torque on the planet is positive, it reverses and we recover migration rates similar to those found in disks where the turbulent viscosity is modelled by an α\alpha viscosity. For the intermediate-mass planets (q=5×105,104q=5\times10^{-5}, 10^{-4} and 2×1042\times10^{-4}) we find a new and so far unexpected behavior. In some cases they experience sustained and systematic outwards migration for the entire duration of the simulation. For this case, the horseshoe region is resolved and torques coming from the corotation region can remain unsaturated due to the stresses in the disk. These stresses are generated directly by the magnetic field. The magnitude of the horseshoe drag can overcome the negative Lindblad contribution when the local surface density profile is flat or increasing outwards, which we see in certain locations in our simulations due to the presence of a zonal flow. The intermediate-mass planet is migrating radially outwards in locations where there is a positive gradient of a pressure bump (zonal flow).Comment: Accepted for publication in Ap
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