Correlation Functions of Warped CFT

Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in WCFT. Similar to conformal symmetry, warped conformal symmetry is very constraining. The form of the two and three point functions are determined by the global warped conformal symmetry while the four point functions can be determined up to an arbitrary function of the cross ratio. The warped conformal bootstrap equation are constructed by formulating the notion of crossing symmetry. In the large central charge limit, four point functions can be decomposed into global warped conformal blocks, which can be solved exactly. Furthermore, we revisit the scattering problem in warped AdS spacetime (WAdS), and give a prescription on how to match the bulk result to a WCFT retarded Green's function. Our result is consistent with the conjectured holographic dualities between WCFT and WAdS.Comment: 20 pages, 0 figur

Entanglement and chaos in warped conformal field theories

Various aspects of warped conformal field theories (WCFTs) are studied including entanglement entropy on excited states, the Renyi entropy after a local quench, and out-of-time-order four-point functions. Assuming a large central charge and dominance of the vacuum block in the conformal block expansion, (i) we calculate the single-interval entanglement entropy on an excited state, matching previous finite temperature results by changing the ensemble; and (ii) we show that WCFTs are maximally chaotic, a result that is compatible with the existence of black holes in the holographic duals. Finally, we relax the aforementioned assumptions and study the time evolution of the Renyi entropy after a local quench. We find that the change in the Renyi entropy is topological, vanishing at early and late times, and nonvanishing in between only for charged states in spectrally-flowed WCFTs.Comment: 31 pages; v2: corrected typos, matches published versio

Modifications to holographic entanglement entropy in warped CFT

In arXiv:1601.02634 it was observed that asymptotic boundary conditions play an important role in the study of holographic entanglement beyond AdS/CFT. In particular, the Ryu-Takayanagi proposal must be modified for warped AdS$_3$ (WAdS$_3$) with Dirichlet boundary conditions. In this paper, we consider AdS$_3$ and WAdS$_3$ with Dirichlet-Neumann boundary conditions. The conjectured holographic duals are warped conformal field theories (WCFTs), featuring a Virasoro-Kac-Moody algebra. We provide a holographic calculation of the entanglement entropy and R\'{e}nyi entropy using AdS$_3$/WCFT and WAdS$_3$/WCFT dualities. Our bulk results are consistent with the WCFT results derived by Castro-Hofman-Iqbal using the Rindler method. Comparing with arXiv:1601.02634, we explicitly show that the holographic entanglement entropy is indeed affected by boundary conditions. Both results differ from the Ryu-Takayanagi proposal, indicating new relations between spacetime geometry and quantum entanglement for holographic dualities beyond AdS/CFT.Comment: 39 pages, 3 figures, published versio

Numerical and experimental study of particle deposition in a tangential inlet cyclone separator

Fluid catalytic cracking (FCC) is an industrial process which converts high-molecular-weight hydrocarbons to lower-molecular-weight products of high value. With the rise of a much heavier fraction in feed, unwanted build-up of carbonaceous deposits onto the surface of the process equipment has been a key process limitation to achieving the economic benefits of longer run length. Hard deposits tend to appear on the outer surface of vortex finder of the secondary cyclones in FCC unit. Literatures have reported that deposits formation is related to the gas flow field. In this study, gas phase flow field in a tangential inlet cyclone was simulated by Large Eddy Simulation, and its effect on deposits buildup was studied by analyzing the forces and secondary flow near the vortex finder wall. The simulated results showed the relationship between flow field and deposits formation. Meanwhile, particle deposition experiment system is setup to investigate the influence of velocity, particle concentration, surface adhesion and length of time on the deposits pattern. Among these experiments, oil-brushed vortex finder wall was studied to imitate an industrial condition in FCC approximately. The experiments offered a more comprehensive study about particle deposition in cyclones. Please click Additional Files below to see the full abstract

Estimating Continuous Muscle Fatigue For Multi-Muscle Coordinated Exercise: A Pilot Study

Assessing the progression of muscle fatigue for daily exercises provides vital indicators for precise rehabilitation, personalized training dose, especially under the context of Metaverse. Assessing fatigue of multi-muscle coordination-involved daily exercises requires the neuromuscular features that represent the fatigue-induced characteristics of spatiotemporal adaptions of multiple muscles and the estimator that captures the time-evolving progression of fatigue. In this paper, we propose to depict fatigue by the features of muscle compensation and spinal module activation changes and estimate continuous fatigue by a physiological rationale model. First, we extract muscle synergy fractionation and the variance of spinal module spikings as features inspired by the prior of fatigue-induced neuromuscular adaptations. Second, we treat the features as observations and develop a Bayesian Gaussian process to capture the time-evolving progression. Third, we solve the issue of lacking supervision information by mathematically formulating the time-evolving characteristics of fatigue as the loss function. Finally, we adapt the metrics that follow the physiological principles of fatigue to quantitatively evaluate the performance. Our extensive experiments present a 0.99 similarity between days, a over 0.7 similarity with other views of fatigue and a nearly 1 weak monotonicity, which outperform other methods. This study would aim the objective assessment of muscle fatigue.Comment: submitted to IEEE JBH