The large N limit of C/Z_N and supergravity

The C/Z_N orbifold of type II string theory has localized tachyons with m^2 ranging from -1+1/N to -2/N in units of 2/\alpha’. We show that by restricting attention to the lightest tachyons it is possible to take a zero-slope limit where N is taken to infinity while N\alpha’ is held fixed. This is done by applying Buscher duality in the angular direction of the cone to obtain a supergravity solution on which the tachyons are gravitational instabilities. In this picture, supergravity provides a natural off-shell description of the tachyonic interactions. For example, the three-point couplings can be read off easily (to leading order in 1/N) from the supergravity action, and are in agreement with the on-shell couplings computed using CFT techniques.