52 research outputs found

    Exact Holography of the Mass-deformed M2-brane Theory

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    We test the holographic relation between the vacuum expectation values of gauge invariant operators in N=6{\cal N} = 6 Uk(N)×Uk(N){\rm U}_k(N)\times {\rm U}_{-k}(N) mass-deformed ABJM theory and the LLM geometries with Zk\mathbb{Z}_k orbifold in 11-dimensional supergravity. To do that, we apply the Kaluza-Klein reduction to construct a 4-dimensional gravity theory and implement the holographic renormalization procedure. We obtain an exact holographic relation for the vacuum expectation values of the chiral primary operator with conformal dimension Δ=1\Delta = 1, which is given by O(Δ=1)=N32f(Δ=1)\langle {\cal O}^{(\Delta=1)}\rangle= N^{\frac32} \, f_{(\Delta=1)}, for large NN and k=1k=1. Here factor f(Δ)f_{(\Delta)} is independent of NN. Our results involve infinite number of exact dual relations for all possible supersymmetric Higgs vacua and so provide a nontrivial test of gauge/gravity duality away from the conformal fixed point. We also extend our results to the case of k1k\ne 1 for LLM geometries represented by rectangular-shaped Young-diagrams.Comment: 6 pages, major corrections in section 3 and 4, references added, title change

    Abelian Gauge Invariance of the WZ-type Coupling in ABJM Theory

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    We construct the interaction terms between the worldvolume fields of multiple M2-branes and 3-form gauge field of 11-dimensional supergravity, in the context of ABJM theory. The obtained Wess-Zumino-type coupling is simultaneously invariant under the UL(N)×_{\textrm{L}}(N)\timesUR(N)_{\textrm{R}}(N) non-Abelian gauge transformation of the ABJM theory and the Abelian gauge transformation of the 3-form field in 11-dimensional supergravity.Comment: 16 pages, minor corrections, published versio

    Gravity from Entanglement and RG Flow in a Top-down Approach

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    The duality between a dd-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdSd+1_{d+1} geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS4_4 gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner. We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS4_4 metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup.Comment: 42 pages, no figure, minor corrections, references adde

    Mass-deformed ABJM Theory and LLM Geometries: Exact Holography

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    We present a detailed account and extension of our claim in arXiv:1610.01490. We test the gauge/gravity duality between the N=6{\cal N} = 6 mass-deformed ABJM theory with Uk(N)×_k(N)\timesUk(N)_{-k}(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)/Zk{\mathbb Z}_k ×\timesSO(4)/Zk{\mathbb Z}_k isometry, in the large NN limit. Our analysis is based on the evaluation of vacuum expectation values of chiral primary operators from the supersymmetric vacua of mass-deformed ABJM theory and from the implementation of Kaluza-Klein holography to the LLM geometries. We focus on the chiral primary operator with conformal dimension Δ=1\Delta = 1. We show that O(Δ=1)=N32f(Δ=1)\langle {\cal O}^{(\Delta=1)}\rangle= N^{\frac32} \, f_{(\Delta=1)} for all supersymmetric vacuum solutions and LLM geometries with k=1k=1, where the factor f(Δ)f_{(\Delta)} is independent of NN. We also confirm that the vacuum expectation value of the the energy momentum tensor is vanishing as expected by the supersymmetry. We extend our results to the case of k1k\ne 1 for LLM geometries represented by rectangular-shaped Young-diagrams. In analogy with the Coulomb branch of the N=4{\cal N} = 4 super Yang-Mills theory, we argue that the discrete Higgs vacua of the mABJM theory as well as the corresponding LLM geometries are parametrized by the vevs of the chiral primary operators.Comment: 44 pages, 1 figure, major corrections in section 3 and 5, references added, title change

    Holography of Massive M2-brane Theory: Non-linear Extension

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    We investigate the gauge/gravity duality between the N=6{\cal N} = 6 mass-deformed ABJM theory with Uk(N)×_k(N)\timesUk(N)_{-k}(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1)×\timesSO(4)/Zk{\mathbb Z}_k ×\timesSO(4)/Zk{\mathbb Z}_k isometry, in terms of a KK holography, which involves quadratic order field redefinitions. As a non-trivial extension of the previous work arXiv:1612.05066, we implement the KK mappings for various gauge invariant fields up to quadratic order to obtain 4-dimensional gravity fields. The non-linearity of the KK maps indicates that, in the current case, we can observe the true purpose of the non-linear KK holography of the LLM solutions. Using such KK holography procedure, we obtain the vacuum expectation values of the chiral primary operator of conformal dimension Δ=2\Delta = 2 in the large NN limit but with general kk and examine the gauge/gravity duality for LLM solutions, which are represented by square-shaped Young diagrams. We also show that the vacuum expectation values of the massive KK graviton modes are vanishing as expected by the supersymmetry.Comment: 27 pages, 2 figures, minor corrections, references adde

    Holography of Massive M2-brane Theory with Discrete Torsion

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    We investigate the gauge/gravity duality between the N=6{\cal N} = 6 mass-deformed ABJ theory with Uk(N+l)×_k(N+l)\timesUk(N)_{-k}(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1)×\timesSO(4)/Zk×{\mathbb Z}_k\timesSO(4)/Zk{\mathbb Z}_k isometry and the discrete torsion ll. For chiral primary operators with conformal dimensions Δ=1,2\Delta=1,2, we obtain the exact vacuum expectation values using the holographic method in 11-dimensional supergravity and show that the results depend on the shapes of droplet pictures in LLM geometries. The lN\frac{l}{\sqrt{N}} contributions from the discrete torsion ll for several simple droplet pictures in the large NN limit are determined in holographic vacuum expectation values. We also explore the effects of the orbifolding Zk{\mathbb Z}_k and the asymptotic discrete torsion ll, on the gauge/gravity duality dictionary and on the nature of the asymptotic limits of the LLM geometries.Comment: 25 pages, 2 figures, The subleading contributions from the field theory calculations are reinterprete

    RAST-K v2-Three-Dimensional Nodal Diffusion Code for Pressurized Water Reactor Core Analysis

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    The RAST-K v2, a novel nodal diffusion code, was developed at the Ulsan National Institute of Science and Technology (UNIST) for designing the cores of pressurized water reactors (PWR) and performing analyses with high accuracy and computational performance by adopting state-of-the-art calculation models and various engineering features. It is a three-dimensional multi-group nodal diffusion code developed for the steady and transient states using microscopic cross-sections generated by the STREAM code for 37 isotopes. A depletion chain containing 22 actinides and 15 fission products and burnable absorbers was solved using the Chebyshev rational approximation method. A simplified one-dimensional single-channel thermal-hydraulic calculation was performed with various values for the thermal conductivity. Advanced features such as burnup adaptation and CRUD modeling capabilities are implemented for the multi-cycle analysis of commercial reactor power plants. The performance of RAST-K v2 has been validated with the measured data of PWRs operating in Korea. Furthermore, RAST-K v2 has been coupled with a sub-channel code (CTF), fuel performance code (FRAPCON), and water chemistry code for multiphysics analyses. In this paper, the calculation models and engineering features implemented in RAST-K v2 are described, and then the application status of RAST-K v2 is presented

    Correction: Jang, D., et al. The Downscaling Study for Typhoon-Induced Coastal Inundation. Water 2020, 12, 1103

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    The authors wish to make the following corrections to this paper [...

    A Broadband PVT-Insensitive All-nMOS Noise-Canceling Balun-LNA for Subgigahertz Wireless Communication Applications

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    A broadband process, voltage, and temperature (PVT)-insensitive noise-canceling balun-low-noise amplifier (LNA) was implemented in the 0.13-μm CMOS process for subgigahertz wireless communication applications. The proposed LNA is based on the traditional common-gate common-source (CGCS) balun-LNA topology, and it adopts the diode-connected loads to reduce the noise contribution originated from CGCS transistors and enhance the linearity due to post linearization. The auxiliary common-source (CS) amplifier with a diode-connected is added to reduce the overall noise figure (NF) of the LNA by sharing an input signal with CGCS transistors and applying its output signal to the diode-connected load of CS transistor. Because the voltage gain of the LNA is determined by the transconductance (gₘ) ratio of the same types of nMOS transistors, its power gain (S₂₁) and NF are quite roust over PVT variations. In experiments, it showed S₂₁ of 14 dB and NF of 4 dB with an input return loss (S₁₁) of greater than 10 dB at 450 MHz. Concerning voltage variation (1.08-1.32 V) and temperature variation (-20 °C ~ +80 °C), the worst variations in S₂₁ and NF were approximately 1.4 and 1.1 dB, respectively. IEEE1
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