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Abstract:

We study monotonicity and other properties of the canonical c-function (defined through the correlator of the energy-momentum tensor) in some holographic duals of 4-d quantum field theories. The canonical c-function and its derivatives are related to the 5d Green's function of the dual supergravity theory. While positivity of the canonical c-function is obvious, we have not found a general proof of its monotonicity, even though c is monotonic in the few explicit examples we examine in this Letter. © 2001 Published by Elsevier Science B.V.

Abstract:

In the context of a five-dimensional brane-world model motivated from heterotic M-theory, we develop a framework for potential-driven brane-world inflation. Specifically this involves a classification of the various background solutions of (A)dS5 type, an analysis of five-dimensional slow-roll conditions and a study of how a transition to the flat vacuum state can be realized. It is shown that solutions with bulk potential and both brane potentials positive exist but are always non-separating and have a non-static orbifold. It turns out that, for this class of backgrounds, a transition to the flat vacuum state during inflation is effectively prevented by the rapidly expanding orbifold. We demonstrate that such a transition can be realized for solutions where one boundary potential is negative. For this case, we present two concrete inflationary models which exhibit the transition explicitly.

Abstract:

We study rolling radii solutions in the context of the four- and five-dimensional effective actions of heterotic M theory. For the standard four-dimensional solutions with varying dilaton and T modulus, we find approximate five-dimensional counterparts. These are new, generically nonseparating solutions corresponding to a pair of five-dimensional domain walls evolving in time. Loop corrections in the four-dimensional theory are described by certain excitations of fields in the fifth dimension. We point out that the two exact separable solutions previously discovered are precisely the special cases for which the loop corrections are time independent. Generically, loop corrections vary with time. Moreover, for a subset of solutions they increase in time, evolving into complicated, nonseparating solutions. In this paper we compute these solutions to leading, nontrivial order. Using the equations for the induced brane metric, we present a general argument showing that the accelerating backgrounds of this type cannot evolve smoothly into decelerating backgrounds. ©2000 The American Physical Society.