Search

Abstract This study explores the use of open educational resources (OERs) in studio-based learning and their influence on learning experiences. The research team conducted action research with 30 bachelor of arts students who were completing a video production subject. Students were required to learn from a website containing open online learning resources under a flipped classroom approach. A teaching schedule and website were designed according to several criteria. Research data were collected through observation, reflective journals, and interviews and were analyzed via thematic analysis. Participating students expressed their perceptions of benefits and hesitation in utilizing OERs in learning. They agreed that the use of OERs as flipped classroom learning materials could positively affect their learning, primarily through competence and learning autonomy as indicated in self-determination theory. This investigation provides teachers with valuable experience and suggestions for teaching and learning approaches that incorporate OERs into studio-based education. Students learn from OERs in which they can gain the most up-to-date technical knowledge in an autonomous environment. This experience indicates that this pedagogy greatly and positively influences students’ subject-learning experiences, learning outcomes, and self-learning skills.

Abstract The Nambu–Jona-Lasinio (NJL) model has been widely studied for investigating the chiral phase structure of strongly interacting matter. The study of the thermodynamics of field theories within the framework of Lattice Field Theory is limited by the sign problem, which prevents Monte Carlo evaluation of the functional integral at a finite chemical potential. Using the quantum imaginary time evolution (QITE) algorithm, we construct a quantum simulation for the (1 + 1) dimensional NJL model at finite temperature and finite chemical potential. We observe consistency among digital quantum simulation, exact diagonalization and analytical solution, indicating further applications of quantum computing in simulating QCD thermodynamics.

Abstract Background Point-of-care ultrasound (POCUS) has emerged as an essential bedside tool for clinicians, but lack of access to ultrasound equipment has been a top barrier to POCUS use. Recently, several handheld ultrasound devices (“handhelds”) have become available, and clinicians are seeking data to guide purchasing decisions. Few comparative studies of different handhelds have been done. We conducted a cross-sectional study comparing 6 handhelds readily available in the United States (Butterfly iQ + ™ by Butterfly Network Inc.; Clarius™ by Clarius Mobile Health; Kosmos™ by EchoNous; TE Air™ by Mindray; Vscan Air™ SL and CL by General Electric; and Lumify™ by Philips Healthcare). A multi-specialty group of physician POCUS experts (n = 35) acquired three standard ultrasound views (abdominal right upper quadrant, cardiac apical 4-chamber, and superficial neck and lung views) in random order on the same standardized patients and rated the image quality. Afterward, a final survey of the overall ease of use, image quality, and satisfaction of each handheld was completed. Results Thirty-five POCUS experts specializing in internal medicine/hospital medicine, critical care, emergency medicine, and nephrology acquired and rated right upper quadrant, apical 4-chamber, and superficial neck and lung views with 6 different handhelds. For image quality, the highest-rated handhelds were Vscan Air™ for the right upper quadrant view, Mindray TE Air™ for the cardiac apical 4-chamber view, and Lumify™ for superficial views of the neck and lung. Overall satisfaction with image quality was highest with Vscan Air™, Lumify™, and Mindray, while overall satisfaction with ease of use was highest with Vscan Air™. The 5 most desirable characteristics of handhelds were image quality, ease of use, portability, probe size, and battery life. Ultimately, all 6 handhelds had notable advantages and disadvantages, with no single device having all desired qualities or features. Conclusions The overall satisfaction with image quality was rated highest with Vscan Air™, Lumify™, and Mindray TE Air™when acquiring right upper quadrant, apical 4-chamber, and superficial neck and lung views. No single handheld was perceived to be superior in image quality for all views. Vscan Air™ was rated highest for overall ease of use and was the most preferred handheld for purchase by POCUS experts.

Abstract What is the bulk Hilbert space of quantum gravity? In this paper, we resolve this problem in 2d JT gravity, both with and without matter, providing an explicit definition of a non-perturbative Hilbert space specified in terms of metric variables. The states are wavefunctions of the length and matter state, but with a non-trivial and highly degenerate inner product. We explicitly identify the null states, and discuss their importance for defining operators non-perturbatively. To highlight the power of the formalism we developed, we study the non-perturbative effects for two bulk linear operators that may serve as proxies for the experience of an observer falling into a two-sided black hole: one captures the length of an Einstein-Rosen bridge and the other captures the center-of-mass collision energy between two particles falling from opposite sides. We track the behavior of these operators up to times of order e S BH $$ {e}^{S_{\textrm{BH}}} $$ , at which point the wavefunction spreads to the complete set of eigenstates of these operators. If these observables are indeed good proxies for the experience of an infalling observer, our results indicate an O(1) probability of detecting a firewall at late times that is self-averaging and universal.

Abstract We study a non-relativistic limit of physics in AdS which retains the curvature through a harmonic Newtonian potential. This limit appears in a CFT dual through the spectrum of operators of large dimension and correlation functions of those operators with appropriate kinematics. In an additional flat spacetime limit, the spectrum is determined by scattering phase shifts (proportional to anomalous dimensions), and a CFT correlation function is proportional to the S-matrix. In particular, we describe the effect of resonances on the spectrum and correlation functions. As an example, we discuss the Coulomb potential (describing solar systems and hydrogen atoms in AdS) in detail.

Abstract In the AdS/CFT correspondence, single trace operators of large-N gauge theories at large spin J can be described by classical spinning strings, giving a geometric and classical description of their spectrum at strong coupling. We observe that in AdS3 these strings have significant gravitational back-reaction at sufficiently large spin, since the gravitational force does not decay at long distances. We construct solutions for folded spinning strings coupled to gravity in AdS3 and compute their spectrum, corresponding to the leading Regge trajectory of Virasroro primary operators. These solutions exist only below a maximal spin J < J max, and as J → J max the solution approaches an extremal rotating BTZ black hole.

Abstract We reformulate recent insights into black hole information in a manner emphasizing operationally-defined notions of entropy, Lorentz-signature descriptions, and asymptotically flat spacetimes. With the help of replica wormholes, we find that experiments of asymptotic observers are consistent with black holes as unitary quantum systems, with density of states given by the Bekenstein-Hawking formula. However, this comes at the cost of superselection sectors associated with the state of baby universes. Spacetimes studied by Polchinski and Strominger in 1994 provide a simple illustration of the associated concepts and techniques, and we argue them to be a natural late-time extrapolation of replica wormholes. The work aims to be self-contained and, in particular, to be accessible to readers who have not yet mastered earlier formulations of the ideas above.

Abstract We propose that a class of new topologies, for which there is no classical solution, should be included in the path integral of three-dimensional pure gravity, and that their inclusion solves pathological negativities in the spectrum, replacing them with a nonperturbative shift of the BTZ extremality bound. We argue that a two dimensional calculation using a dimensionally reduced theory captures the leading effects in the near extremal limit. To make this argument, we study a closely related two-dimensional theory of Jackiw-Teitelboim gravity with dynamical defects. We show that this theory is equivalent to a matrix integral.

Abstract In the 1980’s, work by Coleman and by Giddings and Strominger linked the physics of spacetime wormholes to ‘baby universes’ and an ensemble of theories. We revisit such ideas, using features associated with a negative cosmological constant and asymptotically AdS boundaries to strengthen the results, introduce a change in perspective, and connect with recent replica wormhole discussions of the Page curve. A key new feature is an emphasis on the role of null states. We explore this structure in detail in simple topological models of the bulk that allow us to compute the full spectrum of associated boundary theories. The dimension of the asymptotically AdS Hilbert space turns out to become a random variable Z , whose value can be less than the naive number k of independent states in the theory. For k > Z , consistency arises from an exact degeneracy in the inner product defined by the gravitational path integral, so that many a priori independent states differ only by a null state. We argue that a similar property must hold in any consistent gravitational path integral. We also comment on other aspects of extrapolations to more complicated models, and on possible implications for the black hole information problem in the individual members of the above ensemble.

Abstract We obtain an asymptotic formula for the average value of the operator product expansion coefficients of any unitary, compact two dimensional CFT with c > 1. This formula is valid when one or more of the operators has large dimension or — in the presence of a twist gap — has large spin. Our formula is universal in the sense that it depends only on the central charge and not on any other details of the theory. This result unifies all previous asymptotic formulas for CFT2 structure constants, including those derived from crossing symmetry of four point functions, modular covariance of torus correlation functions, and higher genus modular invariance. We determine this formula at finite central charge by deriving crossing kernels for higher genus crossing equations, which give analytic control over the structure constants even in the absence of exact knowledge of the conformal blocks. The higher genus modular kernels are obtained by sewing together the elementary kernels for four-point crossing and modular transforms of torus one-point functions. Our asymptotic formula is related to the DOZZ formula for the structure constants of Liouville theory, and makes precise the sense in which Liouville theory governs the universal dynamics of heavy operators in any CFT. The large central charge limit provides a link with 3D gravity, where the averaging over heavy states corresponds to a coarse-graining over black hole microstates in holographic theories. Our formula also provides an improved understanding of the Eigenstate Thermalization Hypothesis (ETH) in CFT2, and suggests that ETH can be generalized to other kinematic regimes in two dimensional CFTs.

Abstract We show that an extremely generic class of two-dimensional conformal field theories (CFTs) contains a sector described by the Schwarzian theory. This applies to theories with no additional symmetries and large central charge, but does not require a holographic dual. Specifically, we use bootstrap methods to show that in the grand canonical ensemble, at low temperature with a chemical potential sourcing large angular momentum, the density of states and correlation functions are determined by the Schwarzian theory, up to parametrically small corrections. In particular, we compute out-of-time-order correlators in a controlled approximation. For holographic theories, these results have a gravitational interpretation in terms of large, near-extremal rotating BTZ black holes, which have a near horizon throat with nearly AdS2 × S 1 geometry. The Schwarzian describes strongly coupled gravitational dynamics in the throat, which can be reduced to Jackiw-Teitelboim (JT) gravity interacting with a U(1) field associated to transverse rotations, coupled to matter. We match the physics in the throat to observables at the AdS3 boundary, reproducing the CFT results.

Abstract Any unitary compact two-dimensional CFT with c > 1 and no symmetries beyond Virasoro has a parametrically large density of primary states at large spin for h ¯ $$ \overline{h} $$ > h ¯ extr $$ {\overline{h}}_{\mathrm{extr}} $$ ∼ c − 1 24 $$ \frac{c-1}{24} $$ , of a universal form determined by modular invariance. By including the contribution of light primary operators and multi-twist composites constructed from them in the modular bootstrap, we find that h ¯ extr $$ {\overline{h}}_{\mathrm{extr}} $$ receives corrections in a large spin expansion, which we compute at finite c. The analysis uses a formulation of the modular S-transform as a Fourier transform acting on the density of primary states. For theories with gravitational duals, h ¯ extr $$ {\overline{h}}_{\mathrm{extr}} $$ is interpreted as the extremality bound of rotating BTZ black holes, receiving quantum corrections which we compute at one loop by prohibiting naked singularities in the quantum-corrected geometry. This gravity result is reproduced by modular bootstrap in a semiclassical c → ∞ limit.

Abstract Bulk quantum fields are often said to contribute to the generalized entropy A 4 G N + S bulk $$ \frac{A}{4{G}_N}+{S}_{\mathrm{bulk}} $$ only at O(1). Nonetheless, in the context of evaporating black holes, O(1/GN ) gradients in S bulk can arise due to large boosts, introducing a quantum extremal surface far from any classical extremal surface. We examine the effect of such bulk quantum effects on quantum extremal surfaces (QESs) and the resulting entanglement wedge in a simple two-boundary 2d bulk system defined by Jackiw-Teitelboim gravity coupled to a 1+1 CFT. Turning on a coupling between one boundary and a further external auxiliary system which functions as a heat sink allows a two-sided otherwise-eternal black hole to evaporate on one side. We find the generalized entropy of the QES to behave as expected from general considerations of unitarity, and in particular that ingoing information disappears from the entanglement wedge after a scambling time β 2 π log ΔS + O 1 $$ \frac{\beta }{2\pi}\log \varDelta S+O(1) $$ in accord with expectations for holographic implementations of the Hayden-Preskill protocol. We also find an interesting QES phase transition at what one might call the Page time for our process.

Abstract Every conformal field theory (CFT) above two dimensions contains an infinite set of Regge trajectories of local operators which, at large spin, asymptote to “double-twist” composites with vanishing anomalous dimension. In two dimensions, due to the existence of local conformal symmetry, this and other central results of the conformal bootstrap do not apply. We incorporate exact stress tensor dynamics into the CFT2 analytic bootstrap, and extract several implications for AdS3 quantum gravity. Our main tool is the Virasoro fusion kernel, which we newly analyze and interpret in the bootstrap context. The contribution to double-twist data from the Virasoro vacuum module defines a “Virasoro Mean Field Theory” (VMFT); its spectrum includes a finite number of discrete Regge trajectories, whose dimensions obey a simple formula exact in the central charge c and external operator dimensions. We then show that VMFT provides a baseline for large spin universality in two dimensions: in every unitary compact CFT2 with c > 1 and a twist gap above the vacuum, the double-twist data approaches that of VMFT at large spin ℓ. Corrections to the large spin spectrum from individual non-vacuum primaries are exponentially small in ℓ $$ \sqrt{\ell } $$ for fixed c. We analyze our results in various large c limits. Further applications include a derivation of the late-time behavior of Virasoro blocks at generic c; a refined understanding and new derivation of heavy-light blocks; and the determination of the cross-channel limit of generic Virasoro blocks. We deduce non-perturbative results about the bound state spectrum and dynamics of quantum gravity in AdS3.

Abstract We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure gravity solutions are locally AdS3. This is in addition to the first order Hawking-Page-like phase transitions between different locally AdS3 handlebodies. This implies that the Rényi entropies of holographic CFTs will undergo phase transitions as the Rényi parameter is varied, as long as the theory possesses a scalar operator which is lighter than a certain critical dimension. We show that this critical dimension has an elegant mathematical interpretation as the Hausdorff dimension of the limit set of a quotient group of AdS3, and use this to compute it, analytically near the boundary of moduli space and numerically in the interior of moduli space. We compare this to a CFT computation generalizing recent work of Belin, Keller and Zadeh, bounding the critical dimension using higher genus conformal blocks, and find a surprisingly good match.

Abstract We study the “complexity equals volume” (CV) and “complexity equals action” (CA) conjectures by examining moments of of time symmetry for AdS3 wormholes having n asymptotic regions and arbitrary (orientable) internal topology. For either prescription, the complexity relative to n copies of the M = 0 BTZ black hole takes the form ΔC = αcχ, where c is the central charge and χ is the Euler character of the bulk time-symmetric surface. The coefficients α V = −4π/3, α A = 1/6 defined by CV and CA are independent of both temperature and any moduli controlling the geometry inside the black hole. Comparing with the known structure of dual CFT states in the hot wormhole limit, the temperature and moduli independence of α V , α A implies that any CFT gate set defining either complexity cannot be local. In particular, the complexity of an efficient quantum circuit building local thermofield-double-like entanglement of thermal-sized patches does not depend on the separation of the patches so entangled. We also comment on implications of the (positive) sign found for α A , which requires the associated complexity to decrease when handles are added to our wormhole.

Abstract We derive an asymptotic formula for operator product expansion coefficients of heavy operators in two dimensional conformal field theory. This follows from modular invariance of the genus two partition function, and generalises the asymptotic formula for the density of states from torus modular invariance. The resulting formula is universal, depending only on the central charge, but involves the asymptotic behaviour of genus two conformal blocks. We use monodromy techniques to compute the asymptotics of the relevant blocks at large central charge to determine the behaviour explicitly.

Abstract We give a holographic description of global conformal blocks in two dimensional conformal field theory on the sphere and on the torus. We show that the conformal blocks for one-point functions on the torus can be written as Witten diagrams in thermal AdS. This is accomplished by deriving a general conformal Casimir equation for global conformal blocks, and showing that Witten diagrams obey the same equation. We study the semi-classical limit of n-point conformal blocks, and show that these equal the action of a network of bulk world-lines obeying appropriate geodesic equations. We give an alternate description in the Chern-Simons formulation of 3D gravity, where the conformal blocks are described by networks of Wilson lines, and argue that these formulations are equivalent.

Abstract We investigate the constraints of crossing symmetry on CFT correlation functions. Four point conformal blocks are naturally viewed as functions on the upper-half plane, on which crossing symmetry acts by PSL(2, ℤ $$ \mathbb{Z} $$ ) modular transformations. This allows us to construct a unique, crossing symmetric function out of a given conformal block by averaging over PSL(2, ℤ $$ \mathbb{Z} $$ ). In some two dimensional CFTs the correlation functions are precisely equal to the modular average of the contributions of a finite number of light states. For example, in the two dimensional Ising and tri-critical Ising model CFTs, the correlation functions of identical operators are equal to the PSL(2, ℤ $$ \mathbb{Z} $$ ) average of the Virasoro vacuum block; this determines the 3 point function coefficients uniquely in terms of the central charge. The sum over PSL(2, ℤ $$ \mathbb{Z} $$ ) in CFT2 has a natural AdS3 interpretation as a sum over semi-classical saddle points, which describe particles propagating along rational tangles in the bulk. We demonstrate this explicitly for the correlation function of certain heavy operators, where we compute holographically the semi-classical conformal block with a heavy internal operator.