Holographic Inequalities and Entanglement of Purification

We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.Comment: 17 pages, 4 figures, 1 table. v2: added clarification and fixed typ

A non-trivial spectrum for the trivial \phi^4 theory

It is pointed out that one-component \phi^4 lattice theory in four dimensions has a non-perturbative sector which can be studied by means of an exact duality transformation of its Ising limit. This duality maps it to a membrane model. As a consequence, the \phi^4-theory turns out to have, in the broken symmetry phase, a remarkably rich spectrum of physical states corresponding to membrane excitations. A numerical study of the correlators between dual variables allows to evaluate the masses of the first few states.Comment: 3 pages, talk given at LATTICE'97, Edinburg

Effect of Contrast-Enhanced Echocardiograms on the Prognosis of Infective Endocarditis

Objective - Infective endocarditis (IE) is an infectious disease of the cardiac valves where bacteria colonize the valves; typically, via the formation of vegetations. Recent research has shown that the microbubbles in a contrast-enhanced ultrasound (CEUS) examination can move and dislodge bacterial vegetations in vitro. This study investigated whether CEUS resulted in faster resolution of IE in vivo by dislodging the vegetations. Methods - This IRB approved retrospective study reviewed 36 patients who were diagnosed with IE via echocardiography. Data was sourced from patients within the Jefferson University Hospital’s Cardiology EMR system by searching for contrast and vegetation from January 1st, 2013 – January 1st, 2018. Fifteen patients were not given contrast, whereas 21 patients were given contrast via agitated saline (n=16) or an ultrasound contrast agent (n=5). All patients received an echocardiogram after blood cultures confirmed an infection, but before resolution of infection (defined by negative blood cultures). A student’s t-test was used for analyses. Results - The study population was heterogeneous in terms of sex (67.5% male) and race (70% Caucasian, 25% African American, and 5% Asian), with an average age of 51±20 years, and an average BMI of 29.65±7.43 in the contrast group and 27.67±3.16 in the non-contrast group (p=0.37). Following ultrasound, no patients had documented stroke, pulmonary embolism, or systemic blood clot, which physicians could have attributed to a thrombus resulting from dislodging of bacterial vegetation. Overall, blood cultures did not clear faster in patients receiving CEUS compared to those undergoing standard echocardiography, (2.63±2.69 days vs. 1.34 ±1.11 days, p=0.09). CEUS also did not shorten the admission length in patients with IE, (16.9±7.7 days vs. 19.9±12.1 days; p=0.36). Conclusion - Based on this limited sample size, patients who underwent CEUS did not have a different prognosis when compared to patients who received a non-contrast echocardiogram

Systematic approach to cyclic orbifolds

We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions of conformal field theory and enables us to find the orbifold characters and their modular transformation properties.Comment: 39 pages, LaTeX. v2,3: references added. v4: typos correcte

On the Fixed-Point Structure of Scalar Fields

In a recent Letter (K.Halpern and K.Huang, Phys. Rev. Lett. 74 (1995) 3526), certain properties of the Local Potential Approximation (LPA) to the Wilson renormalization group were uncovered, which led the authors to conclude that $D>2$ dimensional scalar field theories endowed with {\sl non-polynomial} interactions allow for a continuum of renormalization group fixed points, and that around the Gaussian fixed point, asymptotically free interactions exist. If true, this could herald very important new physics, particularly for the Higgs sector of the Standard Model. Continuing work in support of these ideas, has motivated us to point out that we previously studied the same properties and showed that they lead to very different conclusions. Indeed, in as much as the statements in hep-th/9406199 are correct, they point to some deep and beautiful facts about the LPA and its generalisations, but however no new physics.Comment: Typos corrected. A Comment - to be published in Phys. Rev. Lett. 1 page, 1 eps figure, uses LaTeX, RevTex and eps

Asymptotic Charges Cannot Be Measured in Finite Time

To study quantum gravity in asymptotically flat spacetimes, one would like to understand the algebra of observables at null infinity. Here we show that the Bondi mass cannot be observed in finite retarded time, and so is not contained in the algebra on any finite portion of ${\mathscr{I}}^+$. This follows immediately from recently discovered asymptotic entropy bounds. We verify this explicitly, and we find that attempts to measure a conserved charge at arbitrarily large radius in fixed retarded time are thwarted by quantum fluctuations. We comment on the implications of our results to flat space holography and the BMS charges at ${\mathscr{I}}^+$.Comment: 9 pages, 3 figures. v2 typos fixed and minor addition