In this paper, we study theoretically a zero-area Sagnac ring laser gravitational wave (GW) detector. We review first the zero-area Sagnac interferometer for GW detection, comparing its properties against the more conventional GW detector based on a Michaelson interferometer. We then describe a modified version of such a detector where the Sagnac interferometer is replaced by a zero-area Sagnac ring resonator fed by an external laser. This leads to the description of a GW detector based on an active, zero-area Sagnac ring resonator, where a gain medium is present inside the cavity. Finally, we show that if a medium with negative dispersion, which yields the so-called fast-light effect, is also present inside this detector, then its sensitivity to GW strain is enhanced by the inverse of the group index of the dispersive medium. We describe conditions under which this enhancement factor could be as large as 105.