Higher-order logarithmic conformal algebras from Robertson-Walker σ-model backgrounds

We demonstrate that an impulse action ('recoil') on a D-particle embedded in a (four-dimensional) cosmological Robertson-Walker (RW) spacetime is described, in a σ-model framework, by a suitably extended higher-order logarithmic world-sheet algebra of relevant deformations. We study in some detail the algebra of the appropriate two-point correlators, and discuss how can one approach the world-sheet renormalization group infrared fixed point, in the neighborhood of which the logarithmic algebra is valid. Interestingly enough it is found that, if the initial RW spacetime does not have cosmological horizons, then one can define a standard logarithmic algebra to describe the fixed point. However, in the presence of horizons, there are world-sheet divergences, due to relevant operators, which result in the presence of higher-order logarithmic algebras.