Modular invariance and the stability of the AdS soliton

We give a brief review of the bosonic and Type II string models, concentrating on matters of symmetry. In particular, we discuss how modular invariance leads to the GSO projections in the RNS superstring formalism, and contrast the GSO conditions arising from an embedding in flat target space with those arising from an embedding in a toroidally compactified target space. These results are then used to demonstrate the stability of a compact spacetime, the AdS soliton, against the formation of tachyonic winding modes in the low curvature limit. This constitutes further evidence for a positive energy conjecture for asymptotically, locally AdS spacetimes, with the AdS soliton as the minimum energy solution within the context of superstring theory