We define and compute the energy of higher curvature gravity theories in arbitrary dimensions. Generically, these theories admit constant curvature vacua ͑even in the absence of an explicit cosmological constant͒, and asymptotically constant curvature solutions with nontrivial energy properties. For concreteness, we study quadratic curvature models in detail. Among them, the one whose action is the square of the traceless Ricci tensor always has zero energy, unlike conformal ͑Weyl͒ gravity. We also study the string-inspired EinsteinGauss-Bonnet model and show that both its flat and anti-de Sitter vacua are stable.

We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the "cosmological" Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature systems without explicit Lambda-term vacuum must be flat space, and E has the usual Arnowitt-Deser-Misner form. A Lambda-term forces unique de Sitter vacuum, with E the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.

We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D > 4 there are in general two distinct (anti)-de Sitter vacua. We show that for appropriate choice of the parameters there exists a critical point for one of the vacua, for which there are only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl 2 model with a unique vacuum, whose Λ is determined.

We analyze the finite temperature deconfining phase transition in 2+1 dimensional GeorgiGlashow model. We show explicitly that the transition is due to the restoration of the magnetic Z 2 symmetry and that it is in the Ising universality class. We find that neglecting effects of the charged W bosons leads to incorrect predictions for the value of the critical temperature and the universality class of the transition, as well as for various correlation functions in the high temperature phase. We derive the effective action for the Polyakov loop in the high temperature phase and calculate the correlation functions of magnetic vortex operators.PACS:

We define conserved gravitational charges in -cosmologically extended-topologically massive gravity , exhibit them in surface integral form about their de-Sitter or flat vacua and verify their correctness in terms of two basic types of solution.