Ask Mr. Smarty Plants

Sweetgum (Liquidambar styraciflua) is a large, open-crowned tree, sweet-gum grows 75 ft. tall in cultivation and up to 130 ft. in the wild. Large, aromatic tree with straight trunk and conical crown that becomes round and spreading. Young trees are distinctly conical in form. The long, straight trunk is occasionally buttressed and bears strong, ascending branches. Glossy green, deciduous leaves have five deep lobes making a star shape. Fall foliage is purple and red, and will become colorful even without cold temperatures. The fruit is a globular, horny, woody ball, 1 in. in diameter, which hangs on a long stem and persists through January.

Sweet gum can become aggressive in moist, sandy soils. It is not drought-tolerant and does not do well is polluted areas or small areas which limit root development. It grows rapidly and is long-lived, adapting to a variety of sites. It is susceptible to iron chlorosis in soil which is too basic. Plant only in spring as roots take 3-4 months to recover from the shock of transplanting.

Saying this, about one of my favorite trees, it is tough though to grow groundcovers in the dry shade below large trees.

So looking at the Native Plants Database for groundcovers that tolerate dry shade in Tennessee, there are a couple that you might try.  

Lycopodium digitatum (fan clubmoss) likes dry, well drained soils. Though its foliage looks like that of a coniferous plant like pine or juniper, Lycopodium digitatum is in fact a clubmoss, a relative of ferns, with spores instead of seeds. Its cedar-like appearance, low growth (5-10 inches), evergreen leaves, and spreading habit make it ideal for the well-drained eastern woodland landscape. Once established, it spreads quickly by stems that lie just at the surface of the soil.

Potentilla simplex (common cinquefoil) is a familiar plant with prostrate stems, which root at the nodes, and flowers and leaves arising from runners on separate stalks. Runners are 6-20 in. Five-parted leaves and five-petaled, yellow flowers.  Common cinquefoil is a member of the rose family (family Rosaceae). Tolerant to dry shade.

Whatever you plant will need some help with additional water to get the plants established. Good luck!