Beyond a=ca=c: Gravitational Couplings to Matter and the Stress Tensor OPE

We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large $N$ CFTs with a large gap to single-trace higher spin operators, the stress tensor sector is not only universal, but isolated: that is, $\langle TT{\cal O}\rangle=0$, where ${\cal O}\neq T$ is a single-trace primary. We show that this follows from a suppression of $\langle TT{\cal O}\rangle$ by powers of the higher spin gap, $\Delta_{\rm gap}$, dual to the bulk mass scale of higher spin particles, and explain why $\langle TT{\cal O}\rangle$ is a more sensitive probe of $\Delta_{\rm gap}$ than $a-c$ in 4d CFTs. This result implies that, on the level of cubic couplings, the existence of a consistent truncation to Einstein gravity is a direct consequence of the absence of higher spins. By proving similar behavior for other couplings $\langle T{\cal O}_1{\cal O}_2\rangle$ where ${\cal O}_i$ have spin $s_i\leq 2$, we are led to propose that $1/\Delta_{\rm gap}$ is the CFT "dual" of an AdS derivative in a classical action. These results are derived by imposing unitarity on mixed systems of spinning four-point functions in the Regge limit. Using the same method, but without imposing a large gap, we derive new inequalities on these three-point couplings that are valid in any CFT. These are generalizations of the Hofman-Maldacena conformal collider bounds. By combining the collider bound on $TT$ couplings to spin-2 operators with analyticity properties of CFT data, we argue that all three tensor structures of $\langle TTT\rangle$ in the free-field basis are nonzero in interacting CFTs.Comment: 42+25 pages. v2: added refs, minor change

Working in partnership through early support: distance learning text: working with parents in partnership (book chapter)

This is a chapter from the distance learning text for the 'Working in Partnership through Early Support' accredited training programme. "Our intention in this chapter... is to provide a theory of helping, known as the Family Partnership Model. It is based upon the notion that the most effective relationship between parent and helper is a partnership, as first discussed by Mittler, Cunningham and others in the 1970s. It is an explicit and relatively simple framework intended as a guide for all people working with children and their families. Having described the theory, we will look briefly at its implications for service development, training and professional support, the use of the Early Support materials in promoting partnership and the evidence for working in this way." - pp. 2-

Information, sticky prices and macroeconomic foundations : reply to Wright's commentary.

Macroeconomics

Monetary Transmission at Low Inflation: Some Clues from Japan in the 1990s

The paper analyzes the performance of the Japanese economy from 1985 to 1999. It compares different explanations of slow growth and prolonged recession. Using both bivariate comparisons and statistical tests, the paper concludes that the maintained growth rate fill after 1992. Also, the data suggest that the recession early in the 1990s was induced by a decline in money growth. In contrast, the recent recession was induced mainly by a fall in real exports. Failure to allow the nominal exchange rate to depreciate forced deflation and increased the costs of adjusting to reduced export demand The main policy conclusion calls on the Bank of Japan to pursue a more expansive policy to end deflation. This policy would depreciate the yen, but it would end the deflation that is costly to Japan and its neighbors.

Real exchange rates: some evidence from the postwar years

Foreign exchange rates