Note on Weyl versus Conformal Invariance in Field Theory

It was argued recently that conformal invariance in flat spacetime implies Weyl invariance in a general curved background for unitary theories and possible anomalies in the Weyl variation of scalar operators are identified. We argue that generically unitarity alone is not sufficient for a conformal field theory to be Weyl invariant. Furthermore, we show explicitly that when a unitary conformal field theory couples to gravity in a Weyl invariant way, each primary scalar operator that is either relevant or marginal in the unitary conformal field theory corresponds to a Weyl-covariant operator in the curved background.Comment: 10 pages, v3: version to appear in EPJ

Testing for Volatility Changes in Grain Markets

We use newly nonparametric volatility measures and break techniques to estimate common breaks across grain futures over the recent ten years. Our results show one structural change in realized volatilities occurred in 2006 for corn and in 2007 for soybean. But the date difference between them cannot be negligible. We disaggregate the realized volatilities into a continuous component and a jump part and found the source of structural beak in realized volatilities is from jumps.structural change, grain, volatility measures, Financial Economics,