Supergravity, D-brane probes and thermal super Yang-Mills: a comparison

A D3-brane probe in the context of AdS/CFT correspondence at finite tempera ture is considered. The supergravity predictions for the physical effective couplings of the world-volume gauge theory of the probe brane are compared to those calculated in one-loop perturbation theory in the thermal gauge t heory. It is argued that when the Higgs expectation value is much larger th an the temperature, the supergravity result must agree with perturbative th ermal Yang-Mills. This provides a perturbative test of the Maldacena conjec ture. Predictions for the running electric and magnetic effective couplings , beyond perturbation theory are also obtained. Phenomenological applicatio ns for universe-branes are discussed. In particular mechanisms are suggeste d for reducing the induced cosmological constant and naturally obtaining a varying speed of light and a consequent inflation on the universe brane.