Universality in asymptotic bounds and its saturation in 2D CFT

We study asymptotics of three point coefficients (light-light-heavy) and two point correlators in heavy states in unitary, compact 2D CFTs. We prove an upper and lower bound on such quantities using numerically assisted Tauberian techniques. We obtain an optimal upper bound on the spectrum of operators appearing with fixed spin from the OPE of two identical scalars. While all the CFTs obey this bound, rational CFTs come close to saturating it. This mimics the scenario of bounds on asymptotic density of states and thereby pronounces an universal feature in asymptotics of 2D CFTs. Next, we clarify the role of smearing in interpreting the asymptotic results pertaining to considerations of eigenstate thermalization in 2D CFTs. In the context of light-light-heavy three point coefficients, we find that the order one number in the bound is sensitive to how close the light operators are from the $$ \frac{c}{32} $$ c 32 threshold. In context of two point correlator in heavy state, we find the presence of an enigmatic regime which separates the AdS3 thermal physics and the BTZ black hole physics. Furthermore, we present some new numerical results on the behaviour of spherical conformal block.

Phases of scrambling in eigenstates

We use the monodromy method to compute expectation values of an arbitrary number of light operators in finitely excited ("heavy") eigenstates of holographic 2D CFT. For eigenstates with scaling dimensions above the BTZ threshold, these behave thermally up to small corrections, with an effective temperature determined by the heavy state. Below the threshold we find oscillatory and not decaying behavior. As an application of these results we compute the expectation of the out-of-time order arrangement of four light operators in a heavy eigenstate, i.e. a six-point function. Above the threshold we find maximally scrambling behavior with Lyapunov exponent 2\pi T_{eff}2πTeff. Below threshold we find that the eigenstate OTOC shows persistent harmonic oscillations.

Bread and Circuses: Sports and Public Opinion in China

Sports victory constitutes an important part of propaganda in authoritarian states. The heavy state investment in sports industries and sports culture in China illustrates the political importance of sports. However, few studies have systematically examined the exact impact of sports propaganda on public opinion. Using a survey experiment conducted in two Chinese cities, this article finds that broadcast highlighting national sports achievements has significant positive effects on general satisfaction and compliance with the local governments. These results expand on the small, but growing, literature on the effects of sports on political opinions and help detail the specific ways in which sports can affect political attitudes.

American Football Sets Players’ Body Mass Index

Objectives. Document American football, National Football League (NFL), Lean State (LS) or Heavy State (FS) Public High School (PHS), sets similar player position mean body mass indexes (BMI). Review health risks related to BMI. Methods. Public accessible 2014-2015 football rosters were used to calculate individual player’s BMI for four PHS teams about each LS and FS Capital City and 32 NFL teams. Mean BMI were compared for male player positions: quarterback (Q), backfield (B), and line (L) players. Results. Q, B, and L mean BMI were not significantly different for LS and FS PHS and NFL, but mean BMI was significantly ( P < .01) different for Q or B versus L. Conclusion. Football sets similar BMI for player positions with PHS line prone to obese BMI (considered healthy for NFL players) regardless of regional BMI trends. We propose PHS football set player BMI upper limit 30 to support public health and sports safety goals.

The Impact of Globalization on Eurasian Economies: Prospects for Development in the 21st Century

The post-Soviet transformation of Eurasian economies over the past two decades has taken place within the context of the globalization process that has affected many countries around the world. Globalization of capital and transformation of these countries in a market-oriented direction through privatization and joint-ventures with foreign capital has had varied effects in growth and development of Eurasian economies. These developments have taken place at various rates and at varying speeds, depending on the country, especially when one contrasts those in Central Asia with other countries in more developed regions of Eurasia, such as Turkey. In Turkey, a hybrid model of development has evolved over several decades -- one that is built on a strong economic base inherited from the past, where heavy state intervention in the economy has led to the development of a viable industrial infrastructure upon which private capital has expanded and benefited immensely. Thus, the Turkish economy can serve as a model for other Eurasian economies that lack the necessary industrial and financial base, but are able to address the region’s economic problems through a partnership with Turkey. Although a common characteristic of Eurasian economies is the adoption of neoliberal economic policies and integration into the global economy, which often has a negative impact on national economies, a careful approach in engaging with the global economy with heavy state support to guide through the process (as in China) could result in a positive outcome that fosters growth and development of the Eurasian region in the twenty-first century.

Chapter XII Morning Calls

‘Well—I suppose we must.’ Mr. Thornton had had some difficulty in working up his mother to the desired point of civility. She did not often make calls; and when she did, it was in heavy state that...