A note on the Gauge Symmetries of Unimodular Gravity

The symmetries of Unimodular Gravity are clarified somewhat.Comment: 4 pages, v2: acknowledgments correcte

Entanglement loss in molecular quantum-dot qubits due to interaction with the environment

We study quantum entanglement loss due to environmental interaction in a condensed matter system with a complex geometry relevant to recent proposals for computing with single electrons at the nanoscale. We consider a system consisting of two qubits, each realized by an electron in a double quantum dot, which are initially in an entangled Bell state. The qubits are widely separated and each interacts with its own environment. The environment for each is modeled by surrounding double quantum dots placed at random positions with random orientations. We calculate the unitary evolution of the joint system and environment. The global state remains pure throughout. We examine the time dependence of the expectation value of the bipartite Clauser-Horne-Shimony-Holt (CHSH) and Brukner-Paunkovi\'c-Rudolph-Vedral (BPRV) Bell operators and explore the emergence of correlations consistent with local realism. Though the details of this transition depend on the specific environmental geometry, we show how the results can be mapped on to a universal behavior with appropriate scaling. We determine the relevant disentanglement times based on realistic physical parameters for molecular double-dots.Comment: 14 pages, 3 figure

Unimodular Trees versus Einstein Trees

The maximally helicity violating (MHV) tree level scattering amplitudes involving three, four or five gravitons are worked out in Unimodular Gravity. They are found to coincide with the corresponding amplitudes in General Relativity. This a remarkable result, insofar as both the propagators and the vertices are quite different in both theories.Comment: 20 pages, 5 figure

Conformal and non Conformal Dilaton Gravity

The quantum dynamics of the gravitational field non-minimally coupled to an (also dynamical) scalar field is studied in the {\em broken phase}. For a particular value of the coupling the system is classically conformal, and can actually be understood as the group averaging of Einstein-Hilbert's action under conformal transformations. Conformal invariance implies a simple Ward identity asserting that the trace of the equation of motion for the graviton is the equation of motion of the scalar field. We perform an explicit one-loop computation to show that the DeWitt effective action is not UV divergent {\em on shell} and to find that the Weyl symmetry Ward identity is preserved {\em on shell} at that level. We also discuss the fate of this Ward identity at the two-loop level --under the assumption that the two-loop UV divergent part of the effective action can be retrieved from the Goroff-Sagnotti counterterm-- and show that its preservation in the renormalized theory requires the introduction of counterterms which exhibit a logarithmic dependence on the dilaton field.Comment: LateX, 50 pages. Several points clarified; references added. New section on Weyl invariant renormalisation adde

Fiscal Policy and Macroeconomic Uncertainty in Emerging Markets: The Tale of the Tormented Insurer

Governments in emerging markets often behave like a "tormented insurer", trying to use non-state-contingent debt instruments to avoid sharp adjustments in their payments to private agents despite sharp fluctuations in public revenues. In the data, their ability to sustain debt is inversely related to the variability of their revenues, and their primary balances and current expenditures follow a procyclical pattern that contrasts sharply with the evidence from industrial countries. This paper proposes an equilibrium model of a small open economy with incomplete markets and aggregate uncertainty that can rationalize this behavior. In the model, a fiscal authority that chooses optimal expenditure and debt plans given stochastic revenues interacts with private agents that also make optimal consumption and asset accumulation plans. The competitive equilibrium of this economy is solved numerically as a Markov perfect equilibrium using parameter values calibrated to Mexican data. If perfect domestic risk pooling were possible, the ratio of public-to-private expenditures would be constant. With incomplete markets, however, this ratio fluctuates widely and results in welfare losses that dwarf previous estimates of the benefits of risk sharing and consumption smoothing. The model also yields a negative relationship between average public debt and revenue variability similar to the one observed in the data, and a correlation between output and government purchases that matches Mexican dataoptimal debt, fiscal solvency, procyclical fiscal policy, incomplete markets

Public Debt, Fiscal Solvency, and Macroeconomic Uncertainty in Latin America: The Cases of Brazil, Colombia, Costa Rica, and Mexico

The ratios of public debt as a share of GDP of Brazil, Colombia, and Mexico were 12 percentage points higher on average during the period 1996-2005 than in the period 1990-1995. Costa Rica's debt ratio remained stable but at a high level near 50 percent. Is there reason to be concerned for the solvency of the public sector in these economies? We provide an answer to this question based on the quantitative predictions of a variant of the framework proposed by Mendoza and Oviedo (2006). This methodology yields forward-looking estimates of debt ratios that are consistent with fiscal solvency for a government that faces revenue uncertainty and can issue only non-state-contingent debt. In this environment, aversion to a collapse in outlays leads the government to respect a ``natural debt limit" equal to the annuity value of the primary balance in a ``fiscal crisis." A fiscal crisis occurs after a long sequence of adverse revenue shocks and public outlays adjust to their tolerable minimum. The debt limit also represents a credible commitment to remain able to repay even in a fiscal crisis. The debt limit is not, in general, the same as the sustainable debt, which is driven by the probabilistic dynamics of the primary balance. The results of a baseline scenario question the sustainability of current debt ratios in Brazil and Colombia, while those in Costa Rica and Mexico are inside the limits consistent with fiscal solvency. In contrast, current debt ratios are found to be unsustainable in all four countries for plausible changes to lower average growth rates or higher real interest rates. Moreover, sustainable debt ratios fall sharply when default risk is taken into account.

Fiscal Policy and Macroeconomic Uncertainty in Developing Countries: The Tale of the Tormented Insurer

Governments in emerging markets often behave like a "tormented insurer," trying to use non-state-contingent debt instruments to avoid cuts in payments to private agents despite large fluctuations in public revenues. In the data, average public debt-GDP ratios decline as the variability of revenues increases, primary balances and current expenditures follow cyclical patterns sharply at odds with the countercyclical patterns of industrial countries, and the cyclical variability of public expenditures exceeds that of private expenditures by a wide margin. This paper proposes a model of a small open economy with incomplete markets that can rationalize this behavior. In the model a fiscal authority makes optimal expenditure and debt plans given shocks to output and revenues, and private agents make optimal consumption and asset accumulation plans. Quantitative analysis of the model calibrated to Mexico yields a negative relationship between average public debt and revenue variability similar to the one observed in the data. The model mimics Mexico's GDP correlations of government purchases and the primary balance. The ratio of public-to-private expenditures fluctuates widely and the implied welfare costs dwarf conventional estimates of negligible benefits of risk sharing and consumption smoothing.