Conformal invariance beyond the leading order in the supersymmetric nonlinear σ model with dilaton

Abstract

We calculate the 0 (a") contributions to the renormalization-group P functions in the N = 1 supersymmetric u model with a dilaton. At this order both metric and dilaton p functions are found to depend nontrivially on the dilaton field and vanish if the dilaton satisfies V,V,d=O. By employing the Curci-Paffuti relation it is shown that such dilaton backgrounds in Ricci-flat spaces R,,,=O satisfy the conformal invariance conditions up to this order. The particular class of Ricci-flat, compact, and orientable manifolds naturally emerge as appropriate internal-space configurations consistent with local scale invariance. We further explore the cosmological consequences of these dilaton configurations. In a Robertson-Walker four-dimensional background we find all dilatons satisfying V,V,b=O. Except for the constant and the time-dependent dilaton d( t ) = -2 lnt +h whose cosmological implications have been already discussed in the literature, additional solutions are found. These may be of relevance beyond leading order and for nonvanishing background values for the antisymmetric tensor B,,. For these solutions, also the cosmic scale factor is at most linear in time therefore giving rise to either a static or a linearly expanding (contracting) universe.

Tachyon field quantization and Hawking radiation

“…The quadratic terms in the one loop effective action are derived in [10] for any dimension.Especially in two dimensions the diagrammatic derivation of the above non-local terms is simple.In particular the Q 2 term comes from a finite graph.This graph can be evaluated for example in flat space and then the appropriate covariantization yields the result in (10).Furthermore the QR term comes from the contribution of the tadpole graph in the effective action and can be calculated in the same way,as the Q 2 one.The R 2 terms can also be derived diagrammatically in the light-cone gauge.The diagrammatic approach can also used for the derivation of the higher order one-loop terms.The diagrammatic derivation of the form of the effective action is beyond the scope of this paper,so it is not given here.Details for the calculation and covariantization along the above lines,can be found in [11].…”