The large N limit of C/Z_N and supergravity
arXiv:hep-th/0411148 · doi:10.1088/1126-6708/2005/02/054
Abstract
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/α'. 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 Nα' 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.
17 pages, 1 figure; v2: reference added